An Overview of Cryptography

Gary C. Kessler

17 January 2017

© 1998-2017 — A much shorter version of this paper first appeared in Handbook on Local Area Networks (Auerbach, Sept. 1998).
Since that time, this paper has taken on a life of its own...




  1. Three types of cryptography: secret-key, public key, and hash function.
  2. Types of stream ciphers.
  3. Feistel cipher.
  4. Use of the three cryptographic techniques for secure communication.
  5. Kerberos architecture.
  6. VeriSign Class 3 certificate.
  7. Sample entries in Unix/Linux password files.
  8. DES enciphering algorithm.
  9. A PGP signed message.
  10. A PGP encrypted message.
  11. The decrypted message.
  12. IPsec Authentication Header format.
  13. IPsec Encapsulating Security Payload format.
  14. IPsec tunnel and transport modes for AH.
  15. IPsec tunnel and transport modes for ESP.
  16. Keyed-hash MAC operation.
  17. Browser encryption configuration screen (Firefox).
  18. SSL/TLS protocol handshake.
  19. Elliptic curve addition.
  20. AES pseudocode.
  21. TrueCrypt screen shot (Windows).
  22. TrueCrypt screen shot (MacOS).
  23. TrueCrypt hidden encrypted volume within an encrypted volume.
  24. EFS and Windows Explorer.
  25. The cipher command.
  26. EFS key storage.
  27. The $LOGGED_UTILITY_STREAM Attribute.
  28. CHAP Handshake.
  29. Signing and verifying e-mail.
  30. Encrypting and decrypting e-mail.
  31. E-mail message to non-4SecureMail user.
  32. Sample multipart/signed message.
  33. Sample S/MIME encrypted message.
  34. Sample S/MIME certificate.


  1. Minimum Key Lengths for Symmetric Ciphers.
  2. Contents of an X.509 V3 Certificate.
  3. Other Crypto Algorithms and Systems of Note.
  4. ECC and RSA Key Comparison.


Does increased security provide comfort to paranoid people? Or does security provide some very basic protections that we are naive to believe that we don't need? During this time when the Internet provides essential communication between literally billions of people and is used as a tool for commerce, social interaction, and the exchange of an increasing amount of personal information, security has become a tremendously important issue for every user to deal with.

There are many aspects to security and many applications, ranging from secure commerce and payments to private communications and protecting health care information. One essential aspect for secure communications is that of cryptography. But it is important to note that while cryptography is necessary for secure communications, it is not by itself sufficient. The reader is advised, then, that the topics covered here only describe the first of many steps necessary for better security in any number of situations.

This paper has two major purposes. The first is to define some of the terms and concepts behind basic cryptographic methods, and to offer a way to compare the myriad cryptographic schemes in use today. The second is to provide some real examples of cryptography in use today. (See Section A.4 for some additional commentary on this...)

DISCLAIMER: Several companies, products, and services are mentioned in this tutorial. Such mention is for example purposes only and, unless explicitly stated otherwise, should not be taken as a recommendation or endorsement by the author.


Cryptography is the science of secret writing is an ancient art; the first documented use of cryptography in writing dates back to circa 1900 B.C. when an Egyptian scribe used non-standard hieroglyphs in an inscription. Some experts argue that cryptography appeared spontaneously sometime after writing was invented, with applications ranging from diplomatic missives to war-time battle plans. It is no surprise, then, that new forms of cryptography came soon after the widespread development of computer communications. In data and telecommunications, cryptography is necessary when communicating over any untrusted medium, which includes just about any network, particularly the Internet.

There are five primary functions of cryptography today:

  1. Privacy/confidentiality: Ensuring that no one can read the message except the intended receiver.
  2. Authentication: The process of proving one's identity.
  3. Integrity: Assuring the receiver that the received message has not been altered in any way from the original.
  4. Non-repudiation: A mechanism to prove that the sender really sent this message.
  5. Key exchange: The method by which crypto keys are shared between sender and receiver.

In cryptography, we start with the unencrypted data, referred to as plaintext. Plaintext is encrypted into ciphertext, which will in turn (usually) be decrypted into usable plaintext. The encryption and decryption is based upon the type of cryptography scheme being employed and some form of key. For those who like formulas, this process is sometimes written as:

C = Ek(P)
P = Dk(C)

      where P = plaintext, C = ciphertext, E = the encryption method, D = the decryption method, and k = the key.

In many of the descriptions below, two communicating parties will be referred to as Alice and Bob; this is the common nomenclature in the crypto field and literature to make it easier to identify the communicating parties. If there is a third or fourth party to the communication, they will be referred to as Carol and Dave, respectively. A malicious party is referred to as Mallory, an eavesdropper as Eve, and a trusted third party as Trent.

In most common usage, cryptography is most closely associated with the development and creation of the mathematical algorithms used to encrypt and decrypt messages, whereas cryptanalysis is the science of analyzing and breaking encryption schemes. Cryptology is the term referring to the broad study of secret writing, and encompasses both cryptography and cryptanalysis.


There are several ways of classifying cryptographic algorithms. For purposes of this paper, they will be categorized based on the number of keys that are employed for encryption and decryption, and further defined by their application and use. The three types of algorithms that will be discussed are (Figure 1):

FIGURE 1: Three types of cryptography: secret key, public key,
and hash function.

3.1. Secret Key Cryptography

Secret key cryptography methods employ a single key for both encryption and decryption. As shown in Figure 1A, the sender uses the key to encrypt the plaintext and sends the ciphertext to the receiver. The receiver applies the same key to decrypt the message and recover the plaintext. Because a single key is used for both functions, secret key cryptography is also called symmetric encryption.

With this form of cryptography, it is obvious that the key must be known to both the sender and the receiver; that, in fact, is the secret. The biggest difficulty with this approach, of course, is the distribution of the key (more on that later in the discussion of public key cryptography).

Secret key cryptography schemes are generally categorized as being either stream ciphers or block ciphers.

A) Self-synchronizing stream cipher. (From Schneier, 1996, Figure 9.8)

B) Synchronous stream cipher. (From Schneier, 1996, Figure 9.6)

FIGURE 2: Types of stream ciphers.

Stream ciphers operate on a single bit (byte or computer word) at a time and implement some form of feedback mechanism so that the key is constantly changing. Stream ciphers come in several flavors but two are worth mentioning here (Figure 2). Self-synchronizing stream ciphers calculate each bit in the keystream as a function of the previous n bits in the keystream. It is termed "self-synchronizing" because the decryption process can stay synchronized with the encryption process merely by knowing how far into the n-bit keystream it is. One problem is error propagation; a garbled bit in transmission will result in n garbled bits at the receiving side. Synchronous stream ciphers generate the keystream in a fashion independent of the message stream but by using the same keystream generation function at sender and receiver. While stream ciphers do not propagate transmission errors, they are, by their nature, periodic so that the keystream will eventually repeat.

FIGURE 3: Feistel cipher. (Source: Wikimedia Commons)

A block cipher is so-called because the scheme encrypts one block of data at a time using the same key on each block. In general, the same plaintext block will always encrypt to the same ciphertext when using the same key in a block cipher whereas the same plaintext will encrypt to different ciphertext in a stream cipher. The most common construct for block encryption algorithms is the Feistel cipher, named for cryptographer Horst Feistel (IBM). As shown in Figure 3, a Feistel cipher combines elements of substitution, permutation (transposition), and key expansion; these features create a large amount of "confusion and diffusion" (per Claude Shannon) in the cipher. One advantage of the Feistel design is that the encryption and decryption stages are similar, sometimes identical, requiring only a reversal of the key operation, thus dramatically reducing the size of the code (software) or circuitry (hardware) developed to implement the cipher. One of Feistel's early papers describing this operation is "Cryptography and Computer Privacy" (Scientific American, May 1973, 228(5), 15-23).

Block ciphers can operate in one of several modes; the following are the most important:

A good overview of these different modes can be found at CRYPTO-IT.

Secret key cryptography algorithms in use today — or, at least, important today even if not in use — include:

There are several other references that describe interesting algorithms and even SKC codes dating back decades. Two that leap to mind are the Crypto Museum's Crypto List and John J.G. Savard's (albeit old) A Cryptographic Compendium page.

3.2. Public Key Cryptography

Public key cryptography has been said to be the most significant new development in cryptography in the last 300-400 years. Modern PKC was first described publicly by Stanford University professor Martin Hellman and graduate student Whitfield Diffie in 1976. Their paper described a two-key crypto system in which two parties could engage in a secure communication over a non-secure communications channel without having to share a secret key.

PKC depends upon the existence of so-called one-way functions, or mathematical functions that are easy to compute whereas their inverse function is relatively difficult to compute. Let me give you two simple examples:

  1. Multiplication vs. factorization: Suppose you have two prime numbers, 3 and 7, and you need to calculate the product; it should take almost no time to calculate that value, which is 21. Now suppose, instead, that you have a number that is a product of two primes, 21, and you need to determine those prime factors. You will eventually come up with the solution but whereas calculating the product took milliseconds, factoring will take longer. The problem becomes much harder if we start with primes that have, say, 400 digits or so, because the product will have ~800 digits.
  2. Exponentiation vs. logarithms: Suppose you take the number 3 to the 6th power; again, it is relatively easy to calculate 36 = 729. But if you start with the number 729 and need to determine the two integers, x and y so that logx 729 = y, it will take longer to find the two values.

While the examples above are trivial, they do represent two of the functional pairs that are used with PKC; namely, the ease of multiplication and exponentiation versus the relative difficulty of factoring and calculating logarithms, respectively. The mathematical "trick" in PKC is to find a trap door in the one-way function so that the inverse calculation becomes easy given knowledge of some item of information.

Generic PKC employs two keys that are mathematically related although knowledge of one key does not allow someone to easily determine the other key. One key is used to encrypt the plaintext and the other key is used to decrypt the ciphertext. The important point here is that it does not matter which key is applied first, but that both keys are required for the process to work (Figure 1B). Because a pair of keys are required, this approach is also called asymmetric cryptography.

In PKC, one of the keys is designated the public key and may be advertised as widely as the owner wants. The other key is designated the private key and is never revealed to another party. It is straight forward to send messages under this scheme. Suppose Alice wants to send Bob a message. Alice encrypts some information using Bob's public key; Bob decrypts the ciphertext using his private key. This method could be also used to prove who sent a message; Alice, for example, could encrypt some plaintext with her private key; when Bob decrypts using Alice's public key, he knows that Alice sent the message (authentication) and Alice cannot deny having sent the message (non-repudiation).

Public key cryptography algorithms that are in use today for key exchange or digital signatures include:

For additional information on PKC algorithms, see "Public Key Encryption" (Chapter 8) in Handbook of Applied Cryptography, by A. Menezes, P. van Oorschot, and S. Vanstone (CRC Press, 1996).

A digression: Who invented PKC? I tried to be careful in the first paragraph of this section to state that Diffie and Hellman "first described publicly" a PKC scheme. Although I have categorized PKC as a two-key system, that has been merely for convenience; the real criteria for a PKC scheme is that it allows two parties to exchange a secret even though the communication with the shared secret might be overheard. There seems to be no question that Diffie and Hellman were first to publish; their method is described in the classic paper, "New Directions in Cryptography," published in the November 1976 issue of IEEE Transactions on Information Theory (IT-22(6), 644-654). As shown in Section 5.2, Diffie-Hellman uses the idea that finding logarithms is relatively harder than performing exponentiation. And, indeed, it is the precursor to modern PKC which does employ two keys. Rivest, Shamir, and Adleman described an implementation that extended this idea in their paper, "A Method for Obtaining Digital Signatures and Public Key Cryptosystems," published in the February 1978 issue of the Communications of the ACM (CACM) (2192), 120-126). Their method, of course, is based upon the relative ease of finding the product of two large prime numbers compared to finding the prime factors of a large number.

Some sources, though, credit Ralph Merkle with first describing a system that allows two parties to share a secret although it was not a two-key system, per se. A Merkle Puzzle works where Alice creates a large number of encrypted keys, sends them all to Bob so that Bob chooses one at random and then lets Alice know which he has selected. An eavesdropper (Eve) will see all of the keys but can't learn which key Bob has selected (because he has encrypted the response with the chosen key). In this case, Eve's effort to break in is the square of the effort of Bob to choose a key. While this difference may be small it is often sufficient. Merkle apparently took a computer science course at UC Berkeley in 1974 and described his method, but had difficulty making people understand it; frustrated, he dropped the course. Meanwhile, he submitted the paper "Secure Communication Over Insecure Channels," which was published in the CACM in April 1978; Rivest et al.'s paper even makes reference to it. Merkle's method certainly wasn't published first, but did he have the idea first?

An interesting question, maybe, but who really knows? For some time, it was a quiet secret that a team at the UK's Government Communications Headquarters (GCHQ) had first developed PKC in the early 1970s. Because of the nature of the work, GCHQ kept the original memos classified. In 1997, however, the GCHQ changed their posture when they realized that there was nothing to gain by continued silence. Documents show that a GCHQ mathematician named James Ellis started research into the key distribution problem in 1969 and that by 1975, James Ellis, Clifford Cocks, and Malcolm Williamson had worked out all of the fundamental details of PKC, yet couldn't talk about their work. (They were, of course, barred from challenging the RSA patent!) By 1999, Ellis, Cocks, and Williamson began to get their due credit in a break-through article in WIRED Magazine.

And the National Security Agency (NSA) claims to have knowledge of this type of algorithm as early as 1966 but there is no supporting documentation... yet. So this really was a digression...

3.3. Hash Functions

Hash functions, also called message digests and one-way encryption, are algorithms that, in essence, use no key (Figure 1C). Instead, a fixed-length hash value is computed based upon the plaintext that makes it impossible for either the contents or length of the plaintext to be recovered. Hash algorithms are typically used to provide a digital fingerprint of a file's contents, often used to ensure that the file has not been altered by an intruder or virus. Hash functions are also commonly employed by many operating systems to encrypt passwords. Hash functions, then, provide a measure of the integrity of a file.

Let me reiterate that hashes are one-way encryption. You cannot take a hash and "decrypt" it to find the original string that created it, despite the many web sites that claim or suggest otherwise, such as CrackStation,, MD5 Online, md5cracker, OnlineHashCrack, and RainbowCrack.

Note that these sites search databases and/or use rainbow tables to find a suitable string that produces the hash in question but one can't definitively guarantee what string originally produced the hash. This is an important distinction. Suppose that you want to crack someone's password, where the hash of the password is stored on the server. Indeed, all you then need is a string that produces the correct hash and you're in! However, you cannot prove that you have discovered the user's password, only a "duplicate key."

Hash algorithms that are in common use today include:

Readers might be interested in HashCalc, a Windows-based program that calculates hash values using a dozen algorithms, including MD5, SHA-1 and several variants, RIPEMD-160, and Tiger. Command line utilities that calculate hash values include sha_verify by Dan Mares (Windows; supports MD5, SHA-1, SHA-2) and md5deep (cross-platform; supports MD5, SHA-1, SHA-256, Tiger, and Whirlpool).

Hash functions are sometimes misunderstood and some sources claim that no two files can have the same hash value. This is, in theory if not in fact, incorrect. Consider a hash function that provides a 128-bit hash value. There are, then, 2128 possible hash values. But there are an infinite number of possible files and ∞ >> 2128. Therefore, there have to be multiple files — in fact, there have to be an infinite number of files! — that have the same 128-bit hash value.

The difficulty is not necessarily in finding two files with the same hash, but in finding a second file that has the same hash value as a given first file. Consider this example. A human head has, generally, no more than ~150,000 hairs. Since there are more than 7 billion people on earth, we know that there are a lot of people with the same number of hairs on their heads. Finding two people with the same number of hairs, then, would be relatively simple. The harder problem is choosing one person (say, you, the reader) and then finding another person who has the same number of hairs on their head as you have on yours.

This is somewhat similar to the Birthday Problem. We know from probability that if you choose a random group of ~23 people, the probability is about 50% that two will share a birthday (the probability goes up to 99.9% with a group of 70 people). However, if you randomly select one person in a group of 23 and try to find a match to that person, the probability is only about 6% of finding a match; you'd need a group of 253 for a 50% probability of a shared birthday to one of the people chosen at random (and a group of more than 4,000 to obtain a 99.9% probability).

What is hard to do, then, is to try to create a file that matches a given hash value so as to force a hash value collision — which is the reason that hash functions are used extensively for information security and computer forensics applications. Alas, researchers in 2004 found that practical collision attacks could be launched on MD5, SHA-1, and other hash algorithms. Readers interested in this problem should read the following:

Readers are also referred to the Eindhoven University of Technology HashClash Project Web site. An excellent overview of the situation with hash collisions (circa 2005) can be found in RFC 4270 (by P. Hoffman and B. Schneier, November 2005). And for additional information on hash functions, see David Hopwood's MessageDigest Algorithms page and Peter Selinger's MD5 Collision Demo page. Finally, for an interesting twist on this discussion, read about the Nostradamus attack reported at Predicting the winner of the 2008 US Presidential Elections using a Sony PlayStation 3 (by M. Stevens, A.K. Lenstra, and B. de Weger, November 2007).

Certain extensions of hash functions are used for a variety of information security and digital forensics applications, such as:

3.4. Why Three Encryption Techniques?

So, why are there so many different types of cryptographic schemes? Why can't we do everything we need with just one?

The answer is that each scheme is optimized for some specific cryptographic application(s). Hash functions, for example, are well-suited for ensuring data integrity because any change made to the contents of a message will result in the receiver calculating a different hash value than the one placed in the transmission by the sender. Since it is highly unlikely that two different messages will yield the same hash value, data integrity is ensured to a high degree of confidence.

Secret key cryptography, on the other hand, is ideally suited to encrypting messages, thus providing privacy and confidentiality. The sender can generate a session key on a per-message basis to encrypt the message; the receiver, of course, needs the same session key in order to decrypt the message.

Key exchange, of course, is a key application of public key cryptography (no pun intended). Asymmetric schemes can also be used for non-repudiation and user authentication; if the receiver can obtain the session key encrypted with the sender's private key, then only this sender could have sent the message. Public key cryptography could, theoretically, also be used to encrypt messages although this is rarely done because secret key cryptography values can generally be computed about 1000 times faster than public key cryptography values.

FIGURE 4: Use of the three cryptographic techniques for secure communication.

Figure 4 puts all of this together and shows how a hybrid cryptographic scheme combines all of these functions to form a secure transmission comprising a digital signature and digital envelope. In this example, the sender of the message is Alice and the receiver is Bob.

A digital envelope comprises an encrypted message and an encrypted session key. Alice uses secret key cryptography to encrypt her message using the session key, which she generates at random with each session. Alice then encrypts the session key using Bob's public key. The encrypted message and encrypted session key together form the digital envelope. Upon receipt, Bob recovers the session secret key using his private key and then decrypts the encrypted message.

The digital signature is formed in two steps. First, Alice computes the hash value of her message; next, she encrypts the hash value with her private key. Upon receipt of the digital signature, Bob recovers the hash value calculated by Alice by decrypting the digital signature with Alice's public key. Bob can then apply the hash function to Alice's original message, which he has already decrypted (see previous paragraph). If the resultant hash value is not the same as the value supplied by Alice, then Bob knows that the message has been altered; if the hash values are the same, Bob should believe that the message he received is identical to the one that Alice sent.

This scheme also provides nonrepudiation since it proves that Alice sent the message; if the hash value recovered by Bob using Alice's public key proves that the message has not been altered, then only Alice could have created the digital signature. Bob also has proof that he is the intended receiver; if he can correctly decrypt the message, then he must have correctly decrypted the session key meaning that his is the correct private key.

This diagram purposely suggests a cryptosystem where the session key is used for just a single session. Even if this session key is somehow broken, only this session will be compromised; the session key for the next session is not based upon the key for this session, just as this session's key was not dependent on the key from the previous session. This is known as Perfect Forward Secrecy; you might lose one session key due to a compromise but you won't lose all of them. (This was an issue in the 2014 OpenSSL vulnerability known as Heartbleed.)

3.5. The Significance of Key Length

In a 1998 article in the industry literature, a writer made the claim that 56-bit keys did not provide as adequate protection for DES at that time as they did in 1975 because computers were 1000 times faster in 1998 than in 1975. Therefore, the writer went on, we needed 56,000-bit keys in 1998 instead of 56-bit keys to provide adequate protection. The conclusion was then drawn that because 56,000-bit keys are infeasible (true), we should accept the fact that we have to live with weak cryptography (false!). The major error here is that the writer did not take into account that the number of possible key values double whenever a single bit is added to the key length; thus, a 57-bit key has twice as many values as a 56-bit key (because 257 is two times 256). In fact, a 66-bit key would have 1024 times more values than a 56-bit key.

But this does bring up the question, "What is the significance of key length as it affects the level of protection?"

In cryptography, size does matter. The larger the key, the harder it is to crack a block of encrypted data. The reason that large keys offer more protection is almost obvious; computers have made it easier to attack ciphertext by using brute force methods rather than by attacking the mathematics (which are generally well-known anyway). With a brute force attack, the attacker merely generates every possible key and applies it to the ciphertext. Any resulting plaintext that makes sense offers a candidate for a legitimate key. This was the basis, of course, of the EFF's attack on DES.

Until the mid-1990s or so, brute force attacks were beyond the capabilities of computers that were within the budget of the attacker community. By that time, however, significant compute power was typically available and accessible. General-purpose computers such as PCs were already being used for brute force attacks. For serious attackers with money to spend, such as some large companies or governments, Field Programmable Gate Array (FPGA) or Application-Specific Integrated Circuits (ASIC) technology offered the ability to build specialized chips that could provide even faster and cheaper solutions than a PC. As an example, the AT&T Optimized Reconfigurable Cell Array (ORCA) FPGA chip cost about $200 and could test 30 million DES keys per second, while a $10 ASIC chip could test 200 million DES keys per second; compare that to a PC which might be able to test 40,000 keys per second. Distributed attacks, harnessing the power of up to tens of thousands of powerful CPUs, are now commonly employed to try to brute-force crypto keys.

The table below — from a 1995 article discussing both why exporting 40-bit keys was, in essence, no crypto at all and why DES' days were numbered — shows what DES key sizes were needed to protect data from attackers with different time and financial resources. This information was not merely academic; one of the basic tenets of any security system is to have an idea of what you are protecting and from whom are you protecting it! The table clearly shows that a 40-bit key was essentially worthless against even the most unsophisticated attacker. On the other hand, 56-bit keys were fairly strong unless you might be subject to some pretty serious corporate or government espionage. But note that even 56-bit keys were clearly on the decline in their value and that the times in the table were worst cases.

TABLE 1. Minimum Key Lengths for Symmetric Ciphers (1995).
Type of Attacker Budget Tool Time and Cost
Per Key Recovered
Key Length Needed
For Protection
In Late-1995
40 bits 56 bits
Pedestrian Hacker Tiny Scavenged
1 week Infeasible 45
$400 FPGA 5 hours
38 years
Small Business $10,000 FPGA 12 minutes
18 months
Corporate Department $300K FPGA 24 seconds
19 days
ASIC 0.18 seconds
3 hours
Big Company $10M FPGA 7 seconds
13 hours
ASIC 0.005 seconds
6 minutes
Intelligence Agency $300M ASIC 0.0002 seconds
12 seconds

So, how big is big enough? DES, invented in 1975, was still in use at the turn of the century, nearly 25 years later. If we take that to be a design criteria (i.e., a 20-plus year lifetime) and we believe Moore's Law ("computing power doubles every 18 months"), then a key size extension of 14 bits (i.e., a factor of more than 16,000) should be adequate. The 1975 DES proposal suggested 56-bit keys; by 1995, a 70-bit key would have been required to offer equal protection and an 85-bit key necessary by 2015.

A 256- or 512-bit SKC key will probably suffice for some time because that length keeps us ahead of the brute force capabilities of the attackers. Note that while a large key is good, a huge key may not always be better; for example, expanding PKC keys beyond the current 2048- or 4096-bit lengths doesn't add any necessary protection at this time. Weaknesses in cryptosystems are largely based upon key management rather than weak keys.

Much of the discussion above, including the table, is based on the paper "Minimal Key Lengths for Symmetric Ciphers to Provide Adequate Commercial Security" by M. Blaze, W. Diffie, R.L. Rivest, B. Schneier, T. Shimomura, E. Thompson, and M. Wiener (1996).

The most effective large-number factoring methods today use a mathematical Number Field Sieve to find a certain number of relationships and then uses a matrix operation to solve a linear equation to produce the two prime factors. The sieve step actually involves a large number of operations that can be performed in parallel; solving the linear equation, however, requires a supercomputer. Indeed, finding the solution to the RSA-140 challenge in February 1999 — factoring a 140-digit (465-bit) prime number — required 200 computers across the Internet about 4 weeks for the first step and a Cray computer 100 hours and 810 MB of memory to do the second step.

In early 1999, Shamir (of RSA fame) described a new machine that could increase factorization speed by 2-3 orders of magnitude. Although no detailed plans were provided nor is one known to have been built, the concepts of TWINKLE (The Weizmann Institute Key Locating Engine) could result in a specialized piece of hardware that would cost about $5000 and have the processing power of 100-1000 PCs. There still appear to be many engineering details that have to be worked out before such a machine could be built. Furthermore, the hardware improves the sieve step only; the matrix operation is not optimized at all by this design and the complexity of this step grows rapidly with key length, both in terms of processing time and memory requirements. Nevertheless, this plan conceptually puts 512-bit keys within reach of being factored. Although most PKC schemes allow keys that are 1024 bits and longer, Shamir claims that 512-bit RSA keys "protect 95% of today's E-commerce on the Internet." (See Bruce Schneier's Crypto-Gram (May 15, 1999) for more information, as well as the comments from RSA Labs.)

It is also interesting to note that while cryptography is good and strong cryptography is better, long keys may disrupt the nature of the randomness of data files. Shamir and van Someren ("Playing hide and seek with stored keys") have noted that a new generation of viruses can be written that will find files encrypted with long keys, making them easier to find by intruders and, therefore, more prone to attack.

Finally, U.S. government policy has tightly controlled the export of crypto products since World War II. Until the mid-1990s, export outside of North America of cryptographic products using keys greater than 40 bits in length was prohibited, which made those products essentially worthless in the marketplace, particularly for electronic commerce; today, crypto products are widely available on the Internet without restriction. The U.S. Department of Commerce Bureau of Industry and Security maintains an Encryption FAQ web page with more information about the current state of encryption registration.

Without meaning to editorialize too much in this tutorial, a bit of historical context might be helpful. In the mid-1990s, the U.S. Department of Commerce still classified cryptography as a munition and limited the export of any products that contained crypto. For that reason, browsers in the 1995 era, such as Internet Explorer and Netscape, had a domestic version with 128-bit encryption (downloadable only in the U.S.) and an export version with 40-bit encryption. Many cryptographers felt that the export limitations should be lifted because they only applied to U.S. products and seemed to have been put into place by policy makers who believed that only the U.S. knew how to build strong crypto algorithms, ignoring the work ongoing in Australia, Canada, Israel, South Africa, the U.K., and other locations in the 1990s. Those restrictions were lifted by 1996 or 1997, but there is still a prevailing attitude, apparently, that U.S. crypto algorithms are the only strong ones around; consider Bruce Schneier's blog in June 2016 titled "CIA Director John Brennan Pretends Foreign Cryptography Doesn't Exist." Cryptography is a decidedly international game today; note the many countries mentioned above as having developed various algorithms, not the least of which is the fact that NIST's Advanced Encryption Standard employs an algorithm submitted by cryptographers from Belgium. For more evidence, see Schneier's Worldwide Encryption Products Survey (February 2016).

On a related topic, public key crypto schemes can be used for several purposes, including key exchange, digital signatures, authentication, and more. In those PKC systems used for SKC key exchange, the PKC key lengths are chosen so as to be resistant to some selected level of attack. The length of the secret keys exchanged via that system have to have at least the same level of attack resistance. Thus, the three parameters of such a system — system strength, secret key strength, and public key strength — must be matched. This topic is explored in more detail in Determining Strengths For Public Keys Used For Exchanging Symmetric Keys (RFC 3766).


Secure use of cryptography requires trust. While secret key cryptography can ensure message confidentiality and hash codes can ensure integrity, none of this works without trust. In SKC, Alice and Bob had to share a secret key. PKC solved the secret distribution problem, but how does Alice really know that Bob is who he says he is? Just because Bob has a public and private key, and purports to be "Bob," how does Alice know that a malicious person (Mallory) is not pretending to be Bob?

There are a number of trust models employed by various cryptographic schemes. This section will explore three of them:

Each of these trust models differs in complexity, general applicability, scope, and scalability.

4.1. PGP Web of Trust

Pretty Good Privacy (described more below in Section 5.5) is a widely used private e-mail scheme based on public key methods. A PGP user maintains a local keyring of all their known and trusted public keys. The user makes their own determination about the trustworthiness of a key using what is called a "web of trust."

If Alice needs Bob's public key, Alice can ask Bob for it in another e-mail or, in many cases, download the public key from an advertised server; this server might a well-known PGP key repository or a site that Bob maintains himself. In fact, Bob's public key might be stored or listed in many places. (The author's public key, for example, can be found at Alice is prepared to believe that Bob's public key, as stored at these locations, is valid.

Suppose Carol claims to hold Bob's public key and offers to give the key to Alice. How does Alice know that Carol's version of Bob's key is valid or if Carol is actually giving Alice a key that will allow Mallory access to messages? The answer is, "It depends." If Alice trusts Carol and Carol says that she thinks that her version of Bob's key is valid, then Alice may — at her option — trust that key. And trust is not necessarily transitive; if Dave has a copy of Bob's key and Carol trusts Dave, it does not necessarily follow that Alice trusts Dave even if she does trust Carol.

The point here is that who Alice trusts and how she makes that determination is strictly up to Alice. PGP makes no statement and has no protocol about how one user determines whether they trust another user or not. In any case, encryption and signatures based on public keys can only be used when the appropriate public key is on the user's keyring.

4.2. Kerberos

Kerberos is a commonly used authentication scheme on the Internet. Developed by MIT's Project Athena, Kerberos is named for the three-headed dog who, according to Greek mythology, guards the entrance of Hades (rather than the exit, for some reason!).

Kerberos employs a client/server architecture and provides user-to-server authentication rather than host-to-host authentication. In this model, security and authentication will be based on secret key technology where every host on the network has its own secret key. It would clearly be unmanageable if every host had to know the keys of all other hosts so a secure, trusted host somewhere on the network, known as a Key Distribution Center (KDC), knows the keys for all of the hosts (or at least some of the hosts within a portion of the network, called a realm). In this way, when a new node is brought online, only the KDC and the new node need to be configured with the node's key; keys can be distributed physically or by some other secure means.

FIGURE 5: Kerberos architecture.

The Kerberos Server/KDC has two main functions (Figure 5), known as the Authentication Server (AS) and Ticket-Granting Server (TGS). The steps in establishing an authenticated session between an application client and the application server are:

  1. The Kerberos client software establishes a connection with the Kerberos server's AS function. The AS first authenticates that the client is who it purports to be. The AS then provides the client with a secret key for this login session (the TGS session key) and a ticket-granting ticket (TGT), which gives the client permission to talk to the TGS. The ticket has a finite lifetime so that the authentication process is repeated periodically.
  2. The client now communicates with the TGS to obtain the Application Server's key so that it (the client) can establish a connection to the service it wants. The client supplies the TGS with the TGS session key and TGT; the TGS responds with an application session key (ASK) and an encrypted form of the Application Server's secret key; this secret key is never sent on the network in any other form.
  3. The client has now authenticated itself and can prove its identity to the Application Server by supplying the Kerberos ticket, application session key, and encrypted Application Server secret key. The Application Server responds with similarly encrypted information to authenticate itself to the client. At this point, the client can initiate the intended service requests (e.g., Telnet, FTP, HTTP, or e-commerce transaction session establishment).

The current version of this protocol is Kerberos V5 (described in RFC 1510). While the details of their operation, functional capabilities, and message formats are different, the conceptual overview above pretty much holds for both. One primary difference is that Kerberos V4 uses only DES to generate keys and encrypt messages, while V5 allows other schemes to be employed (although DES is still the most widely algorithm used).

4.3. Public Key Certificates and Certificate Authorities

Certificates and Certificate Authorities (CA) are necessary for widespread use of cryptography for e-commerce applications. While a combination of secret and public key cryptography can solve the business issues discussed above, crypto cannot alone address the trust issues that must exist between a customer and vendor in the very fluid, very dynamic e-commerce relationship. How, for example, does one site obtain another party's public key? How does a recipient determine if a public key really belongs to the sender? How does the recipient know that the sender is using their public key for a legitimate purpose for which they are authorized? When does a public key expire? How can a key be revoked in case of compromise or loss?

The basic concept of a certificate is one that is familiar to all of us. A driver's license, credit card, or SCUBA certification, for example, identify us to others, indicate something that we are authorized to do, have an expiration date, and identify the authority that granted the certificate.

As complicated as this may sound, it really isn't. Consider driver's licenses. I have one issued by the State of Florida. The license establishes my identity, indicates the type of vehicles that I can operate and the fact that I must wear corrective lenses while doing so, identifies the issuing authority, and notes that I am an organ donor. When I drive in other states, the other jurisdictions throughout the U.S. recognize the authority of Florida to issue this "certificate" and they trust the information it contains. When I leave the U.S., everything changes. When I am in Aruba, Australia, Canada, Israel, and many other countries, they will accept not the Florida license, per se, but any license issued in the U.S. This analogy represents the certificate trust chain, where even certificates carry certificates.

For purposes of electronic transactions, certificates are digital documents. The specific functions of the certificate include:

Typically, a certificate contains a public key, a name, an expiration date, the name of the authority that issued the certificate (and, therefore, is vouching for the identity of the user), a serial number, any pertinent policies describing how the certificate was issued and/or how the certificate may be used, the digital signature of the certificate issuer, and perhaps other information.

FIGURE 6: VeriSign Class 3 certificate.

A sample abbreviated certificate is shown in Figure 6. This is a typical certificate found in a browser, in this case, Mozilla Firefox (Mac OS X). While this is a certificate issued by VeriSign, many root-level certificates can be found shipped with browsers. When the browser makes a connection to a secure Web site, the Web server sends its public key certificate to the browser. The browser then checks the certificate's signature against the public key that it has stored; if there is a match, the certificate is taken as valid and the Web site verified by this certificate is considered to be "trusted."

TABLE 2. Contents of an X.509 V3 Certificate.
    version number
    certificate serial number
    signature algorithm identifier
    issuer's name and unique identifier
    validity (or operational) period
    subject's name and unique identifier
    subject public key information
    standard extensions
      certificate appropriate use definition
      key usage limitation definition
      certificate policy information
    other extensions

The most widely accepted certificate format is the one defined in International Telecommunication Union Telecommunication Standardization Sector (ITU-T) Recommendation X.509. Rec. X.509 is a specification used around the world and any applications complying with X.509 can share certificates. Most certificates today comply with X.509 Version 3 and contain the information listed in Table 2.

Certificate authorities are the repositories for public keys and can be any agency that issues certificates. A company, for example, may issue certificates to its employees, a college/university to its students, a store to its customers, an Internet service provider to its users, or a government to its constituents.

When a sender needs an intended receiver's public key, the sender must get that key from the receiver's CA. That scheme is straight-forward if the sender and receiver have certificates issued by the same CA. If not, how does the sender know to trust the foreign CA? One industry wag has noted, about trust: "You are either born with it or have it granted upon you." Thus, some CAs will be trusted because they are known to be reputable, such as the CAs operated by AT&T Services, Comodo, DigiCert (formerly GTE Cybertrust), EnTrust, Symantec (formerly VeriSign), and Thawte. CAs, in turn, form trust relationships with other CAs. Thus, if a user queries a foreign CA for information, the user may ask to see a list of CAs that establish a "chain of trust" back to the user.

One major feature to look for in a CA is their identification policies and procedures. When a user generates a key pair and forwards the public key to a CA, the CA has to check the sender's identification and takes any steps necessary to assure itself that the request is really coming from the advertised sender. Different CAs have different identification policies and will, therefore, be trusted differently by other CAs. Verification of identity is just one of many issues that are part of a CA's Certification Practice Statement (CPS) and policies; other issues include how the CA protects the public keys in its care, how lost or compromised keys are revoked, and how the CA protects its own private keys.

As a final note, CAs are not immune to attack and certificates themselves are able to be counterfeited. One of the first such episodes occurred at the turn of the century; on January 29 and 30, 2001, two VeriSign Class 3 code-signing digital certificates were issued to an individual who fraudulently claimed to be a Microsoft employee (CERT/CC CA-2001-04 and Microsoft Security Bulletin MS01-017 - Critical). Problems have continued over the years; good write-ups on this can be found at "Another Certification Authority Breached (the 12th!)" and "How Cybercrime Exploits Digital Certificates." Readers are also urged to read "Certification Authorities Under Attack: A Plea for Certificate Legitimation" (Oppliger, R., January/February 2014, IEEE Internet Computing, 18(1), 40-47).

As a partial way to address this issue, the Internet Security Research Group (ISRG) designed the Automated Certificate Management Environment (ACME) protocol. ACME is a communications protocol that streamlines the process of deploying a Public Key Infrastructure (PKI) by automating interactions between CAs and Web servers that wish to obtain a certificate. More information can be found at the Let's Encrypt Web site, an ACME-based CA service provided by the ISRG.

4.4. Summary

The paragraphs above describe three very different trust models. It is hard to say that any one is better than the others; it depend upon your application. One of the biggest and fastest growing applications of cryptography today, though, is electronic commerce (e-commerce), a term that itself begs for a formal definition.

PGP's web of trust is easy to maintain and very much based on the reality of users as people. The model, however, is limited; just how many public keys can a single user reliably store and maintain? And what if you are using the "wrong" computer when you want to send a message and can't access your keyring? How easy it is to revoke a key if it is compromised? PGP may also not scale well to an e-commerce scenario of secure communication between total strangers on short-notice.

Kerberos overcomes many of the problems of PGP's web of trust, in that it is scalable and its scope can be very large. However, it also requires that the Kerberos server have a priori knowledge of all client systems prior to any transactions, which makes it unfeasible for "hit-and-run" client/server relationships as seen in e-commerce.

Certificates and the collection of CAs will form a PKI. In the early days of the Internet, every host had to maintain a list of every other host; the Domain Name System (DNS) introduced the idea of a distributed database for this purpose and the DNS is one of the key reasons that the Internet has grown as it has. A PKI will fill a similar void in the e-commerce and PKC realm.

While certificates and the benefits of a PKI are most often associated with electronic commerce, the applications for PKI are much broader and include secure electronic mail, payments and electronic checks, Electronic Data Interchange (EDI), secure transfer of Domain Name System (DNS) and routing information, electronic forms, and digitally signed documents. A single "global PKI" is still many years away, that is the ultimate goal of today's work as international electronic commerce changes the way in which we do business in a similar way in which the Internet has changed the way in which we communicate.


The paragraphs above have provided an overview of the different types of cryptographic algorithms, as well as some examples of some available protocols and schemes. Table 3 provides a list of some other noteworthy schemes employed — or proposed — for a variety of functions, most notably electronic commerce and secure communication. The paragraphs below will show several real cryptographic applications that many of us employ (knowingly or not) everyday for password protection and private communication. Some of the schemes described below never were widely deployed but are still historically interesting, thus remain included here.

TABLE 3. Other Crypto Algorithms and Systems of Note.

Capstone A now-defunct U.S. National Institute of Standards and Technology (NIST) and National Security Agency (NSA) project under the Bush Sr. and Clinton administrations for publicly available strong cryptography with keys escrowed by the government (NIST and the Treasury Dept.). Capstone included in one or more tamper-proof computer chips for implementation (Clipper), a secret key encryption algorithm (Skipjack), digital signature algorithm (DSA), key exchange algorithm (KEA), and hash algorithm (SHA).
Challenge-Handshake Authentication Protocol (CHAP) An authentication scheme that allows one party to prove who they are to a second party by demonstrating knowledge of a shared secret without actually divulging that shared secret to a third party who might be listening. Described in RFC 1994.
Clipper The computer chip that would implement the Skipjack encryption scheme. The Clipper chip was to have had a deliberate backdoor so that material encrypted with this device would not be beyond the government's reach. Described in 1993, Clipper was dead by 1996. See also EPIC's The Clipper Chip Web page.
Derived Unique Key Per Transaction (DUKPT) A key management scheme used for debit and credit card verification with point-of-sale (POS) transaction systems, automated teller machines (ATMs), and other financial applications. In DUKPT, a unique key is derived for each transaction based upon a fixed, shared key in such a way that knowledge of one derived key does not easily yield knowledge of other keys (including the fixed key). Therefore, if one of the derived keys is compromised, neither past nor subsequent transactions are endangered. DUKPT is specified in American National Standard (ANS) ANSI X9.24-1:2009 Retail Financial Services Symmetric Key Management Part 1: Using Symmetric Techniques) and can be purchased at the ANSI X9.24 Web page.
Escrowed Encryption Standard (EES) Largely unused, a controversial crypto scheme employing the SKIPJACK secret key crypto algorithm and a Law Enforcement Access Field (LEAF) creation method. LEAF was one part of the key escrow system and allowed for decryption of ciphertext messages that had been intercepted by law enforcement agencies. Described more in FIPS 185 (archived; no longer in force).
Federal Information Processing Standards (FIPS) These computer security- and crypto-related FIPS are produced by the U.S. National Institute of Standards and Technology (NIST) as standards for the U.S. Government.
Fortezza A PCMCIA card developed by NSA that implements the Capstone algorithms, intended for use with the Defense Messaging Service (DMS). Originally called Tessera.
GOST GOST is a family of algorithms that is defined in the Russian cryptographic standards. Although most of the specifications are written in Russian, a series of RFCs describe some of the aspects so that the algorithms can be used effectively in Internet applications:

  • RFC 4357: Additional Cryptographic Algorithms for Use with GOST 28147-89, GOST R 34.10-94, GOST R 34.10-2001, and GOST R 34.11-94 Algorithms
  • RFC 5830: GOST 28147-89: Encryption, Decryption, and Message Authentication Code (MAC) Algorithms
  • RFC 6986: GOST R 34.11-2012: Hash Function Algorithm
  • RFC 7091: GOST R 34.10-2012: Digital Signature Algorithm (Updates RFC 5832: GOST R 34.10-2001)
  • RFC 7801: GOST R 34.12-2015: Block Cipher "Kuznyechik"
  • RFC 7836: Guidelines on the Cryptographic Algorithms to Accompany the Usage of Standards GOST R 34.10-2012 and GOST R 34.11-2012
Identity-Based Encryption (IBE) Identity-Based Encryption was first proposed by Adi Shamir in 1984 and is a key authentication system where the public key can be derived from some unique information based upon the user's identity. In 2001, Dan Boneh (Stanford) and Matt Franklin (U.C., Davis) developed a practical implementation of IBE based on elliptic curves and a mathematical construct called the Weil Pairing. In that year, Clifford Cocks (GCHQ) also described another IBE solution based on quadratic residues in composite groups.

RFC 5091: Identity-Based Cryptography Standard (IBCS) #1: Describes an implementation of IBE using Boneh-Franklin (BF) and Boneh-Boyen (BB1) Identity-based Encryption.
IP Security Protocol (IPsec) The IPsec protocol suite is used to provide privacy and authentication services at the IP layer. An overview of the protocol suite and of the documents comprising IPsec can be found in RFC 2411. Other documents include:
  • RFC 4301: IP security architecture.
  • RFC 4302: IP Authentication Header (AH), one of the two primary IPsec functions; AH provides connectionless integrity and data origin authentication for IP datagrams and protects against replay attacks.
  • RFC 4303: IP Encapsulating Security Payload (ESP), the other primary IPsec function; ESP provides a variety of security services within IPsec.
  • RFC 4304: Extended Sequence Number (ESN) Addendum, allows for negotiation of a 32- or 64- bit sequence number, used to detect replay attacks.
  • RFC 4305: Cryptographic algorithm implementation requirements for ESP and AH.
  • RFC 5996: The Internet Key Exchange (IKE) protocol, version 2, providing for mutual authentication and establishing and maintaining security associations.
    • IKE v1 was described in three separate documents, RFC 2407 (application of ISAKMP to IPsec), RFC 2408 (ISAKMP, a framework for key management and security associations), and RFC 2409 (IKE, using part of Oakley and part of SKEME in conjunction with ISAKMP to obtain authenticated keying material for use with ISAKMP, and for other security associations such as AH and ESP). IKE v1 is obsoleted with the introdcution of IKEv2.
  • RFC 4307: Cryptographic algoritms used with IKEv2.
  • RFC 4308: Crypto suites for IPsec, IKE, and IKEv2.
  • RFC 4309: The use of AES in CBC-MAC mode with IPsec ESP.
  • RFC 4312: The use of the Camellia cipher algorithm in IPsec.
  • RFC 4359: The Use of RSA/SHA-1 Signatures within Encapsulating Security Payload (ESP) and Authentication Header (AH).
  • RFC 4434: Describes AES-XCBC-PRF-128, a pseudo-random function derived from the AES for use with IKE.
  • RFC 2403: Describes use of the HMAC with MD5 algorithm for data origin authentication and integrity protection in both AH and ESP.
  • RFC 2405: Describes use of DES-CBC (DES in Cipher Block Chaining Mode) for confidentiality in ESP.
  • RFC 2410: Defines use of the NULL encryption algorithm (i.e., provides authentication and integrity without confidentiality) in ESP.
  • RFC 2412: Describes OAKLEY, a key determination and distribution protocol.
  • RFC 2451: Describes use of Cipher Block Chaining (CBC) mode cipher algorithms with ESP.
  • RFCs 2522 and 2523: Description of Photuris, a session-key management protocol for IPsec.

In addition, RFC 6379 describes Suite B Cryptographic Suites for IPsec and RFC 6380 describes the Suite B profile for IPsec.

IPsec was first proposed for use with IP version 6 (IPv6), but can also be employed with the current IP version, IPv4.

(See more detail about IPsec below in Section 5.6.)

Internet Security Association and Key Management Protocol (ISAKMP/OAKLEY) ISAKMP/OAKLEY provide an infrastructure for Internet secure communications. ISAKMP, designed by the National Security Agency (NSA) and described in RFC 2408, is a framework for key management and security associations, independent of the key generation and cryptographic algorithms actually employed. The OAKLEY Key Determination Protocol, described in RFC 2412, is a key determination and distribution protocol using a variation of Diffie-Hellman.
Kerberos A secret key encryption and authentication system, designed to authenticate requests for network resources within a user domain rather than to authenticate messages. Kerberos also uses a trusted third-party approach; a client communications with the Kerberos server to obtain "credentials" so that it may access services at the application server. Kerberos V4 used DES to generate keys and encrypt messages; Kerberos V5 uses DES and other schemes for key generation.

Microsoft added support for Kerberos V5 — with some proprietary extensions — in Windows 2000 Active Directory. There are many Kerberos articles posted at Microsoft's Knowledge Base, notably "Kerberos Explained."
Keyed-Hash Message Authentication Code (HMAC) A message authentication scheme based upon secret key cryptography and the secret key shared between two parties rather than public key methods. Described in FIPS 198 and RFC 2104. (See Section 5.6 below for details on HMAC operation.)
Message Digest Cipher (MDC) Invented by Peter Gutman, MDC turns a one-way hash function into a block cipher.
MIME Object Security Services (MOSS) Designed as a successor to PEM to provide PEM-based security services to MIME messages. Described in RFC 1848. Never widely implemented and now defunct.
Mujahedeen Secrets A Windows GUI, PGP-like crytosystem. Developed by supporters of Al-Qaeda, the program employs the five finalist AES algorithms, namely, MARS, RC6, Rijndael, Serpent, and Twofish. Also described in Inspire Magazine, Issue 1, pp. 41-44 and Inspire Magazine, Issue 2, pp. 58-59. Additional related information can also be found in "How Al-Qaeda Uses Encryption Post-Snowden (Part 2)."
NSA Suite B Cryptography An NSA standard for securing information at the SECRET level. Defines use of:
  • Advanced Encryption Standard (AES) with key sizes of 128 and 256 bits, per FIPS PUB 197 for encryption
  • The Ephemeral Unified Model and the One-Pass Diffie Hellman (referred to as ECDH) using the curves with 256 and 384-bit prime moduli, per NIST Special Publication 800-56A for key exchange
  • Elliptic Curve Digital Signature Algorithm (ECDSA) using the curves with 256 and 384-bit prime moduli, per FIPS PUB 186-3 for digital signatures
  • Secure Hash Algorithm (SHA) using 256 and 384 bits, per FIPS PUB 180-3 for hashing

RFC 6239 describes Suite B Cryptographic Suites for Secure Shell (SSH) and RFC 6379 describes Suite B Cryptographic Suites for Secure IP (IPsec).

Pretty Good Privacy (PGP) A family of cryptographic routines for e-mail, file, and disk encryption developed by Philip Zimmermann. PGP 2.6.x uses RSA for key management and digital signatures, IDEA for message encryption, and MD5 for computing the message's hash value; more information can also be found in RFC 1991. PGP 5.x (formerly known as "PGP 3") uses Diffie-Hellman/DSS for key management and digital signatures; IDEA, CAST, or 3DES for message encryption; and MD5 or SHA for computing the message's hash value. OpenPGP, described in RFC 2440, is an open definition of security software based on PGP 5.x. The GNU Privacy Guard (GPG) is a free software version of OpenPGP.

(See more detail about PGP below in Section 5.5.)

Privacy Enhanced Mail (PEM) An IETF standard for secure electronic mail over the Internet, including provisions for encryption (DES), authentication, and key management (DES, RSA). Developed by the IETF but never widely used. Described in the following RFCs:
  • RFC 1421: Part I, Message Encryption and Authentication Procedures
  • RFC 1422: Part II, Certificate-Based Key Management
  • RFC 1423: Part III, Algorithms, Modes, and Identifiers
  • RFC 1424: Part IV, Key Certification and Related Services
Private Communication Technology (PCT) Developed by Microsoft for secure communication on the Internet. PCT supported Diffie-Hellman, Fortezza, and RSA for key establishment; DES, RC2, RC4, and triple-DES for encryption; and DSA and RSA message signatures. Never widely used; superceded by SSL and TLS.
Secure Electronic Transaction (SET) A communications protocol for securing credit card transactions, developed by MasterCard and VISA, in cooperation with IBM, Microsoft, RSA, and other companies. Merged two other protocols: Secure Electronic Payment Protocol (SEPP), an open specification for secure bank card transactions over the Internet developed by CyberCash, GTE, IBM, MasterCard, and Netscape; and Secure Transaction Technology (STT), a secure payment protocol developed by Microsoft and Visa International. Supports DES and RC4 for encryption, and RSA for signatures, key exchange, and public key encryption of bank card numbers. SET V1.0 is described in Book 1, Book 2, and Book 3. SET has been superceded by SSL and TLS.
Secure Hypertext Transfer Protocol (S-HTTP) An extension to HTTP to provide secure exchange of documents over the World Wide Web. Supported algorithms include RSA and Kerberos for key exchange, DES, IDEA, RC2, and Triple-DES for encryption. Described in RFC 2660. S-HTTP was never as widely used as HTTP over SSL (https).
Secure Multipurpose Internet Mail Extensions (S/MIME) An IETF secure e-mail scheme superceding PEM, and adding digital signature and encryption capability to Internet MIME messages. S/MIME Version 3.1 is described in RFCs 3850 and 3851, and employs the Cryptographic Message Syntax described in RFCs 3369 and 3370.

(More detail about S/MIME can be found below in Section 5.15.)
Secure Sockets Layer (SSL) Developed by Netscape Communications to provide application-independent security and privacy over the Internet. SSL is designed so that protocols such as HTTP, FTP (File Transfer Protocol), and Telnet can operate over it transparently. SSL allows both server authentication (mandatory) and client authentication (optional). RSA is used during negotiation to exchange keys and identify the actual cryptographic algorithm (DES, IDEA, RC2, RC4, or 3DES) to use for the session. SSL also uses MD5 for message digests and X.509 public key certificates. SSL was found to be breakable soon after the IETF announced formation of group to work on TLS and RFC 6176 specifically prohibits the use of SSL v2.0 by TLS clients. SSL version 3.0 is described in RFC 6101. All versions of SSL are now deprecated in favor of TLS; TLS v1.0 is sometimes referred to as "SSL v3.1."

(More detail about SSL can be found below in Section 5.7.)
Server Gated Cryptography (SGC) Microsoft extension to SSL that provides strong encryption for online banking and other financial applications using RC2 (128-bit key), RC4 (128-bit key), DES (56-bit key), or 3DES (equivalent of 168-bit key). Use of SGC requires a Windows NT Server running Internet Information Server (IIS) 4.0 with a valid SGC certificate. SGC is available in 32-bit Windows versions of Internet Explorer (IE) 4.0, and support for Mac, Unix, and 16-bit Windows versions of IE is expected in the future.
Simple Authentication and Security Layer (SASL) A framework for providing authentication and data security services in connection-oriented protocols (a la TCP), described in RFC 4422. It provides a structured interface and allows new protocols to reuse existing authentication mechanisms and allows old protocols to make use of new mechanisms.

It has been common practice on the Internet to permit anonymous access to various services, employing a plain-text password using a user name of "anonymous" and a password of an email address or some other identifying information. New IETF protocols disallow plain-text logins. The Anonymous SASL Mechanism (RFC 4505) provides a method for anonymous logins within the SASL framework.
Simple Key-Management for Internet Protocol (SKIP) Key management scheme for secure IP communication, specifically for IPsec, and designed by Aziz and Diffie. SKIP essentially defines a public key infrastructure for the Internet and even uses X.509 certificates. Most public key cryptosystems assign keys on a per-session basis, which is inconvenient for the Internet since IP is connectionless. Instead, SKIP provides a basis for secure communication between any pair of Internet hosts. SKIP can employ DES, 3DES, IDEA, RC2, RC5, MD5, and SHA-1. As it happened, SKIP was not adopted for IPsec; IKE was selected instead.
Transport Layer Security (TLS) TLS v1.0 is an IETF specification (RFC 2246) intended to replace SSL v3.0. TLS v1.0 employs Triple-DES (secret key cryptography), SHA (hash), Diffie-Hellman (key exchange), and DSS (digital signatures). TLS v1.0 was vulnerable to attack and updated by v1.1 (RFC 4346) and v1.2 (RFC 5246); v1.3 is the most current working draft specification.

TLS is designed to operate over TCP. The IETF developed the Datagram Transport Layer Security (DTLS) protocol to operate over UDP. DTLS v1.2 is described in RFC 6347.

(See more detail about TLS below in Section 5.7.)

TrueCrypt Open source, multi-platform cryptography software that can be used to encrypt a file, partition, or entire disk. One of TrueCrypt's more interesting features is that of plausible deniability with hidden volumes or hidden operating systems. The original Web site,, suddenly went dark in May 2014; alternative sites have popped up, including CipherShed, TCnext, and VeraCrypt.

(See more detail about TrueCrypt below in Section 5.11.)

X.509 ITU-T recommendation for the format of certificates for the public key infrastructure. Certificates map (bind) a user identity to a public key. The IETF application of X.509 certificates is documented in RFC 5280. An Internet X.509 Public Key Infrastructure is further defined in RFC 4210 (Certificate Management Protocols) and RFC 3647 (Certificate Policy and Certification Practices Framework).

5.1. Password Protection

Nearly all modern multiuser computer and network operating systems employ passwords at the very least to protect and authenticate users accessing computer and/or network resources. But passwords are not typically kept on a host or server in plaintext, but are generally encrypted using some sort of hash scheme.

A) /etc/passwd file

 carol:FM5ikbQt1K052:502:100:Carol Monaghan:/home/carol:/bin/bash
 alex:LqAi7Mdyg/HcQ:503:100:Alex Insley:/home/alex:/bin/bash
 gary:FkJXupRyFqY4s:501:100:Gary Kessler:/home/gary:/bin/bash
 todd:edGqQUAaGv7g6:506:101:Todd Pritsky:/home/todd:/bin/bash
 josh:FiH0ONcjPut1g:505:101:Joshua Kessler:/home/webroot:/bin/bash

B.1) /etc/passwd file (with shadow passwords)

 carol:x:502:100:Carol Monaghan:/home/carol:/bin/bash
 alex:x:503:100:Alex Insley:/home/alex:/bin/bash
 gary:x:501:100:Gary Kessler:/home/gary:/bin/bash
 todd:x:506:101:Todd Pritsky:/home/todd:/bin/bash
 josh:x:505:101:Joshua Kessler:/home/webroot:/bin/bash

B.2) /etc/shadow file


FIGURE 7: Sample entries in Unix/Linux password files.

Unix/Linux, for example, uses a well-known hash via its crypt() function. Passwords are stored in the /etc/passwd file (Figure 7A); each record in the file contains the username, hashed password, user's individual and group numbers, user's name, home directory, and shell program; these fields are separated by colons (:). Note that each password is stored as a 13-byte string. The first two characters are actually a salt, randomness added to each password so that if two users have the same password, they will still be encrypted differently; the salt, in fact, provides a means so that a single password might have 4096 different encryptions. The remaining 11 bytes are the password hash, calculated using DES.

As it happens, the /etc/passwd file is world-readable on Unix systems. This fact, coupled with the weak encryption of the passwords, resulted in the development of the shadow password system where passwords are kept in a separate, non-world-readable file used in conjunction with the normal password file. When shadow passwords are used, the password entry in /etc/passwd is replaced with a "*" or "x" (Figure 7B.1) and the MD5 hash of the passwords are stored in /etc/shadow along with some other account information (Figure 7B.2).

Windows NT uses a similar scheme to store passwords in the Security Access Manager (SAM) file. In the NT case, all passwords are hashed using the MD4 algorithm, resulting in a 128-bit (16-byte) hash value (they are then obscured using an undocumented mathematical transformation that was a secret until distributed on the Internet). The password password, for example, might be stored as the hash value (in hexadecimal) 60771b22d73c34bd4a290a79c8b09f18.

Passwords are not saved in plaintext on computer systems precisely so they cannot be easily compromised. For similar reasons, we don't want passwords sent in plaintext across a network. But for remote logon applications, how does a client system identify itself or a user to the server? One mechanism, of course, is to send the password as a hash value and that, indeed, may be done. A weakness of that approach, however, is that an intruder can grab the password off of the network and use an off-line attack (such as a dictionary attack where an attacker takes every known word and encrypts it with the network's encryption algorithm, hoping eventually to find a match with a purloined password hash). In some situations, an attacker only has to copy the hashed password value and use it later on to gain unauthorized entry without ever learning the actual password.

An even stronger authentication method uses the password to modify a shared secret between the client and server, but never allows the password in any form to go across the network. This is the basis for the Challenge Handshake Authentication Protocol (CHAP), the remote logon process used by Windows NT.

As suggested above, Windows NT passwords are stored in a security file on a server as a 16-byte hash value. In truth, Windows NT stores two hashes; a weak hash based upon the old LAN Manager (LanMan) scheme and the newer NT hash. When a user logs on to a server from a remote workstation, the user is identified by the username, sent across the network in plaintext (no worries here; it's not a secret anyway!). The server then generates a 64-bit random number and sends it to the client (also in plaintext). This number is the challenge.

Using the LanMan scheme, the client system then encrypts the challenge using DES. Recall that DES employs a 56-bit key, acts on a 64-bit block of data, and produces a 64-bit output. In this case, the 64-bit data block is the random number. The client actually uses three different DES keys to encrypt the random number, producing three different 64-bit outputs. The first key is the first seven bytes (56 bits) of the password's hash value, the second key is the next seven bytes in the password's hash, and the third key is the remaining two bytes of the password's hash concatenated with five zero-filled bytes. (So, for the example above, the three DES keys would be 60771b22d73c34, bd4a290a79c8b0, and 9f180000000000.) Each key is applied to the random number resulting in three 64-bit outputs, which comprise the response. Thus, the server's 8-byte challenge yields a 24-byte response from the client and this is all that would be seen on the network. The server, for its part, does the same calculation to ensure that the values match.

There is, however, a significant weakness to this system. Specifically, the response is generated in such a way as to effectively reduce 16-byte hash to three smaller hashes, of length seven, seven, and two, respectively. Thus, a password cracker has to break at most a 7-byte hash. One Windows NT vulnerability test program that I used in the past reported passwords that were "too short," defined as "less than 8 characters." When I asked how the program knew that passwords were too short, the software's salespeople suggested to me that the program broke the passwords to determine their length. This was, in fact, not the case at all; all the software really had to do was to look at the last eight bytes of the Windows NT LanMan hash to see that the password was seven or fewer characters.

Consider the following example, showing the LanMan hash of two different short passwords (take a close look at the last 8 bytes):

AA: 89D42A44E77140AAAAD3B435B51404EE
AAA: 1C3A2B6D939A1021AAD3B435B51404EE

Note that the NT hash provides no such clue:

AA: C5663434F963BE79C8FD99F535E7AAD8
AAA: 6B6E0FB2ED246885B98586C73B5BFB77

It is worth noting that the discussion above describes the Microsoft version of CHAP, or MS-CHAP (MS-CHAPv2 is described in RFC 2759). MS-CHAP assumes that it is working with hashed values of the password as the key to encrypting the challenge. More traditional CHAP (RFC 1994) assumes that it is starting with passwords in plaintext. The relevance of this observation is that a CHAP client, for example, cannot be authenticated by an MS-CHAP server; both client and server must use the same CHAP version.

5.2. Some of the Finer Details of Diffie-Hellman

Diffie and Hellman introduced the concept of public key cryptography. The mathematical "trick" of Diffie-Hellman key exchange is that it is relatively easy to compute exponents compared to computing discrete logarithms. Diffie-Hellman allows two parties — the ubiquitous Alice and Bob — to generate a secret key; they need to exchange some information over an unsecure communications channel to perform the calculation but an eavesdropper cannot determine the shared secret key based upon this information.

Diffie-Hellman works like this. Alice and Bob start by agreeing on a large prime number, N. They also have to choose some number G so that G<N.

There is actually another constraint on G, namely that it must be primitive with respect to N. Primitive is a definition that is a little beyond the scope of our discussion but basically G is primitive to N if the set of N-1 values of Gi mod N for i = (1,N-1) are all different. As an example, 2 is not primitive to 7 because the set of powers of 2 from 1 to 6, mod 7 (i.e., 21 mod 7, 22 mod 7, ..., 26 mod 7) = {2,4,1,2,4,1}. On the other hand, 3 is primitive to 7 because the set of powers of 3 from 1 to 6, mod 7 = {3,2,6,4,5,1}.

(The definition of primitive introduced a new term to some readers, namely mod. The phrase x mod y (and read as written!) means "take the remainder after dividing x by y." Thus, 1 mod 7 = 1, 9 mod 6 = 3, and 8 mod 8 = 0. Read more about the modulo function in the appendix.)

Anyway, either Alice or Bob selects N and G; they then tell the other party what the values are. Alice and Bob then work independently:


  1. Choose a large random number, XA < N. This is Alice's private key.
  2. Compute YA = GXA mod N. This is Alice's public key.
  3. Exchange public key with Bob.
  4. Compute KA = YBXA mod N

  1. Choose a large random number, XB < N. This is Bob's private key.
  2. Compute YB = GXB mod N. This is Bob's public key.
  3. Exchange public key with Alice.
  4. Compute KB = YAXB mod N

Note that XA and XB are kept secret while YA and YB are openly shared; these are the private and public keys, respectively. Based on their own private key and the public key learned from the other party, Alice and Bob have computed their secret keys, KA and KB, respectively, which are equal to GXAXB mod N.

Perhaps a small example will help here. Although Alice and Bob will really choose large values for N and G, I will use small values for example only; let's use N=7 and G=3.


  1. Choose XA = 2
  2. Calculate YA = 32 mod 7 = 2
  3. Exchange public keys with Bob
  4. KA = 62 mod 7 = 1

  1. Choose XB = 3
  2. Calculate YB = 33 mod 7 = 6
  3. Exchange public keys with Alice
  4. KB = 23 mod 7 = 1

In this example, then, Alice and Bob will both find the secret key 1 which is, indeed, 36 mod 7 (i.e., GXAXB = 32x3). If an eavesdropper (Mallory) was listening in on the information exchange between Alice and Bob, he would learn G, N, YA, and YB which is a lot of information but insufficient to compromise the key; as long as XA and XB remain unknown, K is safe. As said above, calculating Y = GX is a lot easier than finding X = logG Y.

A short digression on modulo arithmetic. In the paragraph above, we noted that 36 mod 7 = 1. This can be confirmed, of course, by noting that:

36 = 729 = 104*7 + 1

There is a nice property of modulo arithmetic, however, that makes this determination a little easier, namely: (a mod x)(b mod x) = (ab mod x). Therefore, one possible shortcut is to note that 36 = (33)(33). Therefore, 36 mod 7 = (33 mod 7)(33 mod 7) = (27 mod 7)(27 mod 7) = 6*6 mod 7 = 36 mod 7 = 1.

Diffie-Hellman can also be used to allow key sharing amongst multiple users. Note again that the Diffie-Hellman algorithm is used to generate secret keys, not to encrypt and decrypt messages.

5.3. Some of the Finer Details of RSA Public Key Cryptography

Unlike Diffie-Hellman, RSA can be used for key exchange as well as digital signatures and the encryption of small blocks of data. Today, RSA is primarily used to encrypt the session key used for secret key encryption (message integrity) or the message's hash value (digital signature). RSA's mathematical hardness comes from the ease in calculating large numbers and the difficulty in finding the prime factors of those large numbers. Although employed with numbers using hundreds of digits, the math behind RSA is relatively straight-forward.

To create an RSA public/private key pair, here are the basic steps:

  1. Choose two prime numbers, p and q. From these numbers you can calculate the modulus, n = pq.
  2. Select a third number, e, that is relatively prime to (i.e., it does not divide evenly into) the product (p-1)(q-1). The number e is the public exponent.
  3. Calculate an integer d from the quotient (ed-1)/[(p-1)(q-1)]. The number d is the private exponent.

The public key is the number pair (n,e). Although these values are publicly known, it is computationally infeasible to determine d from n and e if p and q are large enough.

To encrypt a message, M, with the public key, create the ciphertext, C, using the equation:

The receiver then decrypts the ciphertext with the private key using the equation:

Now, this might look a bit complex and, indeed, the mathematics does take a lot of computer power given the large size of the numbers; since p and q may be 100 digits (decimal) or more, d and e will be about the same size and n may be over 200 digits. Nevertheless, a simple example may help. In this example, the values for p, q, e, and d are purposely chosen to be very small and the reader will see exactly how badly these values perform, but hopefully the algorithm will be adequately demonstrated:

  1. Select p=3 and q=5.
  2. The modulus n = pq = 15.
  3. The value e must be relatively prime to (p-1)(q-1) = (2)(4) = 8. Select e=11.
  4. The value d must be chosen so that (ed-1)/[(p-1)(q-1)] is an integer. Thus, the value (11d-1)/[(2)(4)] = (11d-1)/8 must be an integer. Calculate one possible value, d=3.
  5. Let's suppose that we want to send a message — maybe a secret key — that has the numeric value of 7 (i.e., M=7). [More on this choice below.]
  6. The sender encrypts the message (M) using the public key value (e,n)=(11,15) and computes the ciphertext (C) with the formula C = 711 mod 15 = 1977326743 mod 15 = 13.
  7. The receiver decrypts the ciphertext using the private key value (d,n)=(3,15) and computes the plaintext with the formula M = 133 mod 15 = 2197 mod 15 = 7.

I choose this trivial example because the value of n is so small (in particular, the value M cannot exceed n). But here is a more realistic example using larger d, e, and n values, as well as a more meaningful message; thanks to Barry Steyn for permission to use values from his How RSA Works With Examples page.

Let's say that we have chosen p and q so that we have the following value for n:


Let's also suppose that we have selected the public key, e, and private key, d, as follows:



Now suppose that our message (M) is the character string "attack at dawn" which has the numeric value (after converting the ASCII characters to a bit string and interpreting that bit string as a decimal number) of 1976620216402300889624482718775150.

The encryption phase uses the formula C = Me mod n, so C has the value:


The decryption phase uses the formula M = Cd mod n, so M has the value that matches our original plaintext:


This more realistic example gives just a clue as to how large the numbers are that are used in the real world implementations. RSA keylengths of 512 and 768 bits are considered to be pretty weak. The minimum suggested RSA key is 1024 bits; 2048 and 3072 bits are even better.

As an aside, Adam Back ( wrote a two-line Perl script to implement RSA. It employs dc, an arbitrary precision arithmetic package that ships with most UNIX systems:

print pack"C*",split/\D+/,`echo "16iII*o\U@{$/=$z;[(pop,pop,unpack"H*",<>

5.4. Some of the Finer Details of DES, Breaking DES, and DES Variants

The Data Encryption Standard (DES) started life in the mid-1970s, adopted by the National Bureau of Standards (NBS) [now the National Institute for Standards and Technology (NIST)] as Federal Information Processing Standard 46 (FIPS 46-3) and by the American National Standards Institute (ANSI) as X3.92.

As mentioned earlier, DES uses the Data Encryption Algorithm (DEA), a secret key block-cipher employing a 56-bit key operating on 64-bit blocks. FIPS 81 describes four modes of DES operation: Electronic Codebook (ECB), Cipher Block Chaining (CBC), Cipher Feedback (CFB), and Output Feedback (OFB). Despite all of these options, ECB is the most commonly deployed mode of operation.

NIST finally declared DES obsolete in 2004, and withdrew FIPS 46-3, 74, and 81 (Federal Register, July 26, 2004, 69(142), 44509-44510). Although other block ciphers have replaced DES, it is still interesting to see how DES encryption is performed; not only is it sort of neat, but DES was the first crypto scheme commonly seen in non-governmental applications and was the catalyst for modern "public" cryptography and the first public Feistel cipher. DES still remains in many products — and cryptography students and cryptographers will continue to study DES for years to come.

DES Operational Overview

DES uses a 56-bit key. In fact, the 56-bit key is divided into eight 7-bit blocks and an 8th odd parity bit is added to each block (i.e., a "0" or "1" is added to the block so that there are an odd number of 1 bits in each 8-bit block). By using the 8 parity bits for rudimentary error detection, a DES key is actually 64 bits in length for computational purposes although it only has 56 bits worth of randomness, or entropy (See Section A.3 for a brief discussion of entropy and information theory).

FIGURE 8: DES enciphering algorithm.

DES then acts on 64-bit blocks of the plaintext, invoking 16 rounds of permutations, swaps, and substitutes, as shown in Figure 8. The standard includes tables describing all of the selection, permutation, and expansion operations mentioned below; these aspects of the algorithm are not secrets. The basic DES steps are:

  1. The 64-bit block to be encrypted undergoes an initial permutation (IP), where each bit is moved to a new bit position; e.g., the 1st, 2nd, and 3rd bits are moved to the 58th, 50th, and 42nd position, respectively.

  2. The 64-bit permuted input is divided into two 32-bit blocks, called left and right, respectively. The initial values of the left and right blocks are denoted L0 and R0.

  3. There are then 16 rounds of operation on the L and R blocks. During each iteration (where n ranges from 1 to 16), the following formulae apply:

      Ln = Rn-1
      Rn = Ln-1 XOR f(Rn-1,Kn)

    At any given step in the process, then, the new L block value is merely taken from the prior R block value. The new R block is calculated by taking the bit-by-bit exclusive-OR (XOR) of the prior L block with the results of applying the DES cipher function, f, to the prior R block and Kn. (Kn is a 48-bit value derived from the 64-bit DES key. Each round uses a different 48 bits according to the standard's Key Schedule algorithm.)

    The cipher function, f, combines the 32-bit R block value and the 48-bit subkey in the following way. First, the 32 bits in the R block are expanded to 48 bits by an expansion function (E); the extra 16 bits are found by repeating the bits in 16 predefined positions. The 48-bit expanded R-block is then ORed with the 48-bit subkey. The result is a 48-bit value that is then divided into eight 6-bit blocks. These are fed as input into 8 selection (S) boxes, denoted S1,...,S8. Each 6-bit input yields a 4-bit output using a table lookup based on the 64 possible inputs; this results in a 32-bit output from the S-box. The 32 bits are then rearranged by a permutation function (P), producing the results from the cipher function.

  4. The results from the final DES round — i.e., L16 and R16 — are recombined into a 64-bit value and fed into an inverse initial permutation (IP-1). At this step, the bits are rearranged into their original positions, so that the 58th, 50th, and 42nd bits, for example, are moved back into the 1st, 2nd, and 3rd positions, respectively. The output from IP-1 is the 64-bit ciphertext block.

Consider this example using DES in CBC mode with the following 56-bit key and input:

    Key: 1100101 0100100 1001001 0011101 0110101 0101011 1101100 0011010 = 0x6424491D352B6C1A

    Input character string (ASCII/IA5): +2903015-08091765
    Input string (hex): 0x2B323930333031352D3038303931373635

    Output string (hex): 0x9812CB620B2E9FD3AD90DE2B92C6BBB6C52753AC43E1AFA6
    Output character string (BASE64): mBLLYgsun9OtkN4rksa7tsUnU6xD4a+m

Observe that we start with a 17-byte input message. DES acts on eight bytes at a time, so this message is padded to 24 bytes and provides three "inputs" to the cipher algorithm (we don't see the padding here; it is appended by the DES code). Since we have three input blocks, we get 24 bytes of output from the three 64-bit (eight byte) output blocks.

If you want to test this, a really good free, online DES calculator run by the University of Cambridge Computer Laboratory. An excellent step-by-step example of DES can also be found at J. Orlin Grabbe's The DES Algorithm Illustrated page.

NOTE: You'll notice that the output above is shown in BASE64. BASE64 is a 64-character alphabet — i.e., a six-bit character code composed of upper- and lower-case letters, the digits 0-9, and a few punctuation characters — that is commonly used as a way to display binary data. A byte has eight bits, or 256 values, but not all 256 ASCII characters are defined and/or printable. BASE64, simply, takes a binary string (or file), divides it into six-bit blocks, and translates each block into a printable character. More information about BASE64 can be found at my BASE64 Alphabet page or at Wikipedia.

Breaking DES

The mainstream cryptographic community has long held that DES's 56-bit key was too short to withstand a brute-force attack from modern computers. Remember Moore's Law: computer power doubles every 18 months. Given that increase in power, a key that could withstand a brute-force guessing attack in 1975 could hardly be expected to withstand the same attack a quarter century later.

DES is even more vulnerable to a brute-force attack because it is often used to encrypt words, meaning that the entropy of the 64-bit block is, effectively, greatly reduced. That is, if we are encrypting random bit streams, then a given byte might contain any one of 28 (256) possible values and the entire 64-bit block has 264, or about 18.5 quintillion, possible values. If we are encrypting words, however, we are most likely to find a limited set of bit patterns; perhaps 70 or so if we account for upper and lower case letters, the numbers, space, and some punctuation. This means that only about ¼ of the bit combinations of a given byte are likely to occur.

Despite this criticism, the U.S. government insisted throughout the mid-1990s that 56-bit DES was secure and virtually unbreakable if appropriate precautions were taken. In response, RSA Laboratories sponsored a series of cryptographic challenges to prove that DES was no longer appropriate for use.

DES Challenge I was launched in March 1997. It was completed in 84 days by R. Verser in a collaborative effort using thousands of computers on the Internet.

The first DES Challenge II lasted 40 days in early 1998. This problem was solved by, a worldwide distributed computing network using the spare CPU cycles of computers around the Internet (participants in's activities load a client program that runs in the background, conceptually similar to the SETI @Home "Search for Extraterrestrial Intelligence" project). The systems were checking 28 billion keys per second by the end of the project.

The second DES Challenge II lasted less than 3 days. On July 17, 1998, the Electronic Frontier Foundation (EFF) announced the construction of hardware that could brute-force a DES key in an average of 4.5 days. Called Deep Crack, the device could check 90 billion keys per second and cost only about $220,000 including design (it was erroneously and widely reported that subsequent devices could be built for as little as $50,000). Since the design is scalable, this suggests that an organization could build a DES cracker that could break 56-bit keys in an average of a day for as little as $1,000,000. Information about the hardware design and all software can be obtained from the EFF.

The DES Challenge III, launched in January 1999, was broken is less than a day by the combined efforts of Deep Crack and This is widely considered to have been the final nail in DES's coffin.

The Deep Crack algorithm is actually quite interesting. The general approach that the DES Cracker Project took was not to break the algorithm mathematically but instead to launch a brute-force attack by guessing every possible key. A 56-bit key yields 256, or about 72 quadrillion, possible values. So the DES cracker team looked for any shortcuts they could find! First, they assumed that some recognizable plaintext would appear in the decrypted string even though they didn't have a specific known plaintext block. They then applied all 256 possible key values to the 64-bit block (I don't mean to make this sound simple!). The system checked to see if the decrypted value of the block was "interesting," which they defined as bytes containing one of the alphanumeric characters, space, or some punctuation. Since the likelihood of a single byte being "interesting" is about ¼, then the likelihood of the entire 8-byte stream being "interesting" is about ¼8, or 1/65536 (½16). This dropped the number of possible keys that might yield positive results to about 240, or about a trillion.

They then made the assumption that an "interesting" 8-byte block would be followed by another "interesting" block. So, if the first block of ciphertext decrypted to something interesting, they decrypted the next block; otherwise, they abandoned this key. Only if the second block was also "interesting" did they examine the key closer. Looking for 16 consecutive bytes that were "interesting" meant that only 224, or 16 million, keys needed to be examined further. This further examination was primarily to see if the text made any sense. Note that possible "interesting" blocks might be 1hJ5&aB7 or DEPOSITS; the latter is more likely to produce a better result. And even a slow laptop today can search through lists of only a few million items in a relatively short period of time. (Interested readers are urged to read Cracking DES and EFF's Cracking DES page.)

It is well beyond the scope of this paper to discuss other forms of breaking DES and other codes. Nevertheless, it is worth mentioning a couple of forms of cryptanalysis that have been shown to be effective against DES. Differential cryptanalysis, invented in 1990 by E. Biham and A. Shamir (of RSA fame), is a chosen-plaintext attack. By selecting pairs of plaintext with particular differences, the cryptanalyst examines the differences in the resultant ciphertext pairs. Linear plaintext, invented by M. Matsui, uses a linear approximation to analyze the actions of a block cipher (including DES). Both of these attacks can be more efficient than brute force.

DES Variants

Once DES was "officially" broken, several variants appeared. But none of them came overnight; work at hardening DES had already been underway. In the early 1990s, there was a proposal to increase the security of DES by effectively increasing the key length by using multiple keys with multiple passes. But for this scheme to work, it had to first be shown that the DES function is not a group, as defined in mathematics. If DES was a group, then we could show that for two DES keys, X1 and X2, applied to some plaintext (P), we can find a single equivalent key, X3, that would provide the same result; i.e.,

EX2(EX1(P)) = EX3(P)

where EX(P) represents DES encryption of some plaintext P using DES key X. If DES were a group, it wouldn't matter how many keys and passes we applied to some plaintext; we could always find a single 56-bit key that would provide the same result.

As it happens, DES was proven to not be a group so that as we apply additional keys and passes, the effective key length increases. One obvious choice, then, might be to use two keys and two passes, yielding an effective key length of 112 bits. Let's call this Double-DES. The two keys, Y1 and Y2, might be applied as follows:

C = EY2(EY1(P))
P = DY1(DY2(C))

where EY(P) and DY(C) represent DES encryption and decryption, respectively, of some plaintext P and ciphertext C, respectively, using DES key Y.

So far, so good. But there's an interesting attack that can be launched against this "Double-DES" scheme. First, notice that the applications of the formula above can be thought of with the following individual steps (where C' and P' are intermediate results):

C' = EY1(P) and C = EY2(C')
P' = DY2(C) and P = DY1(P')

Unfortunately, C'=P'. That leaves us vulnerable to a simple known plaintext attack (sometimes called "Meet-in-the-middle") where the attacker knows some plaintext (P) and its matching ciphertext (C). To obtain C', the attacker needs to try all 256 possible values of Y1 applied to P; to obtain P', the attacker needs to try all 256 possible values of Y2 applied to C. Since C'=P', the attacker knows when a match has been achieved — after only 256 + 256 = 257 key searches, only twice the work of brute-forcing DES. So "Double-DES" is not a good solution.

Triple-DES (3DES), based upon the Triple Data Encryption Algorithm (TDEA), is described in FIPS 46-3. 3DES, which is not susceptible to a meet-in-the-middle attack, employs three DES passes and one, two, or three keys called K1, K2, and K3. Generation of the ciphertext (C) from a block of plaintext (P) is accomplished by:

C = EK3(DK2(EK1(P)))

where EK(P) and DK(P) represent DES encryption and decryption, respectively, of some plaintext P using DES key K. (For obvious reasons, this is sometimes referred to as an encrypt-decrypt-encrypt mode operation.)

Decryption of the ciphertext into plaintext is accomplished by:

P = DK1(EK2(DK3(C)))

The use of three, independent 56-bit keys provides 3DES with an effective key length of 168 bits. The specification also defines use of two keys where, in the operations above, K3 = K1; this provides an effective key length of 112 bits. Finally, a third keying option is to use a single key, so that K3 = K2 = K1 (in this case, the effective key length is 56 bits and 3DES applied to some plaintext, P, will yield the same ciphertext, C, as normal DES would with that same key). Given the relatively low cost of key storage and the modest increase in processing due to the use of longer keys, the best recommended practices are that 3DES be employed with three keys.

Another variant of DES, called DESX, is due to Ron Rivest. Developed in 1996, DESX is a very simple algorithm that greatly increases DES's resistance to brute-force attacks without increasing its computational complexity. In DESX, the plaintext input is XORed with 64 additional key bits prior to encryption and the output is likewise XORed with the 64 key bits. By adding just two XOR operations, DESX has an effective keylength of 120 bits against an exhaustive key-search attack. As it happens, DESX is no more immune to other types of more sophisticated attacks, such as differential or linear cryptanalysis, but brute-force is the primary attack vector on DES.

Closing Comments

Although DES has been deprecated and replaced by the Advanced Encryption Standard (AES) because of its vulnerability to a modestly-priced brute-force attack, many applications continue to rely on DES for security, and many software designers and implementers continue to include DES in new applications. In some cases, use of DES is wholly appropriate but, in general, DES should not continue to be promulgated in production software and hardware. RFC 4772 discusses the security implications of employing DES.

On a final note, readers may be interested in seeing an Excel implementation of DES or J.O. Grabbe's The DES Algorithm Illustrated.

5.5. Pretty Good Privacy (PGP)

Pretty Good Privacy (PGP) is one of today's most widely used public key cryptography programs. Developed by Philip Zimmermann in the early 1990s and long the subject of controversy, PGP is available as a plug-in for many e-mail clients, such as Apple Mail (with GPG), Eudora Email, Microsoft Outlook/Outlook Express, and Mozilla Thunderbird (with Enigmail).

PGP can be used to sign or encrypt e-mail messages with the mere click of the mouse. Depending upon the version of PGP, the software uses SHA or MD5 for calculating the message hash; CAST, Triple-DES, or IDEA for encryption; and RSA or DSS/Diffie-Hellman for key exchange and digital signatures.

When PGP is first installed, the user has to create a key-pair. One key, the public key, can be advertised and widely circulated. The private key is protected by use of a passphrase. The passphrase has to be entered every time the user accesses their private key.

 Hash: SHA512

 Hi Carol.

 What was that pithy Groucho Marx quote?


Comment: GPGTools -


FIGURE 9: A PGP signed message. The sender uses their private key; at the destination, the sender's e-mail address yields the public key from the receiver's keyring.

Figure 9 shows a PGP signed message. This message will not be kept secret from an eavesdropper, but a recipient can be assured that the message has not been altered from what the sender transmitted. In this instance, the sender signs the message using their own private key. The receiver uses the sender's public key to verify the signature; the public key is taken from the receiver's keyring based on the sender's e-mail address. Note that the signature process does not work unless the sender's public key is on the receiver's keyring.

Comment: GPGTools -


FIGURE 10: A PGP encrypted message. The receiver's e-mail address is the pointer to the public key in the sender's keyring. At the destination side, the receiver uses their own private key.

Figure 10 shows a PGP encrypted message (PGP compresses the file, where practical, prior to encryption because encrypted files have a high degree of randomness and, therefore, cannot be efficiently compressed). In this example, public key methods are used to exchange the session key for the actual message encryption that employs secret-key cryptography. In this case, the receiver's e-mail address is the pointer to the public key in the sender's keyring; in fact, the same message can be sent to multiple recipients and the message will not be significantly longer since all that needs to be added is the session key encrypted by each receiver's public key. When the message is received, the recipient will use their private key to extract the session secret key to successfully decrypt the message (Figure 11).

Hi Gary,

"Outside of a dog, a book is man's best friend.
Inside of a dog, it's too dark to read."


FIGURE 11: The decrypted message.

It is worth noting that PGP was one of the first so-called "hybrid cryptosystems" that combined aspects of SKC and PKC. When Zimmermann was first designing PGP in the late-1980s, he wanted to use RSA to encrypt the entire message. The PCs of the days, however, suffered significant performance degradation when executing RSA so he hit upon the idea of using SKC to encrypt the message and PKC to encrypt the SKC key.

PGP went into a state of flux in 2002. Zimmermann sold PGP to Network Associates, Inc. (NAI) in 1997 and then resigned from NAI in early 2001. In March 2002, NAI announced that they were dropping support for the commercial version of PGP having failed to find a buyer for the product willing to pay what they wanted. In August 2002, PGP was purchased from NAI by PGP Corp. which, in turn, was purchased by Symantec. Meanwhile, there are many freeware versions of PGP available through the International PGP Page and the OpenPGP Alliance. Also check out the GNU Privacy Guard (GnuPG), a GNU project implementation of OpenPGP (defined in RFC 2440); GnuPG is also know as GPG.

5.6. IP Security (IPsec) Protocol

NOTE: The information in this section assumes that the reader is familiar with the Internet Protocol (IP), at least to the extent of the packet format and header contents. More information about IP can be found in An Overview of TCP/IP Protocols and the Internet. More information about IPv6 can be found in IPv6: The Next Generation Internet Protocol.

The Internet and the TCP/IP protocol suite were not built with security in mind. This is not meant as a criticism but as an observation; the baseline IP, TCP, UDP, and ICMP protocols were written in 1980 and built for the relatively closed ARPANET community. TCP/IP wasn't designed for the commercial-grade financial transactions that they now see or for virtual private networks (VPNs) on the Internet. To bring TCP/IP up to today's security necessities, the Internet Engineering Task Force (IETF) formed the IP Security Protocol Working Group which, in turn, developed the IP Security (IPsec) protocol. IPsec is not a single protocol, in fact, but a suite of protocols providing a mechanism to provide data integrity, authentication, privacy, and nonrepudiation for the classic Internet Protocol (IP). Although intended primarily for IP version 6 (IPv6), IPsec can also be employed by the current version of IP, namely IP version 4 (IPv4).

As shown in Table 3, IPsec is described in nearly a dozen RFCs. RFC 4301, in particular, describes the overall IP security architecture and RFC 2411 provides an overview of the IPsec protocol suite and the documents describing it.

IPsec can provide either message authentication and/or encryption. The latter requires more processing than the former, but will probably end up being the preferred usage for applications such as VPNs and secure electronic commerce.

Central to IPsec is the concept of a security association (SA). Authentication and confidentiality using AH or ESP use SAs and a primary role of IPsec key exchange it to establish and maintain SAs. An SA is a simplex (one-way or unidirectional) logical connection between two communicating IP endpoints that provides security services to the traffic carried by it using either AH or ESP procedures. The endpoint of an SA can be an IP host or IP security gateway (e.g., a proxy server, VPN server, etc.). Providing security to the more typical scenario of two-way (bi-directional) communication between two endpoints requires the establishment of two SAs (one in each direction).

An SA is uniquely identified by a 3-tuple composed of:

The IP Authentication Header (AH), described in RFC 4302, provides a mechanism for data integrity and data origin authentication for IP packets using HMAC with MD5 (RFC 2403), HMAC with SHA-1 (RFC 2404), or HMAC with RIPEMD (RFC 2857). See also RFC 4305.

    0                   1                   2                   3
    0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
   | Next Header   |  Payload Len  |          RESERVED             |
   |                 Security Parameters Index (SPI)               |
   |                    Sequence Number Field                      |
   |                                                               |
   +                Integrity Check Value-ICV (variable)           |
   |                                                               |

FIGURE 12: IPsec Authentication Header format. (From RFC 4302)

Figure 12 shows the format of the IPsec AH. The AH is merely an additional header in a packet, more or less representing another protocol layer above IP (this is shown in Figure 14 below). Use of the IP AH is indicated by placing the value 51 (0x33) in the IPv4 Protocol or IPv6 Next Header field in the IP packet header. The AH follows mandatory IPv4/IPv6 header fields and precedes higher layer protocol (e.g., TCP, UDP) information. The contents of the AH are:

The IP Encapsulating Security Payload (ESP), described in RFC 4303, provides message integrity and privacy mechanisms in addition to authentication. As in AH, ESP uses HMAC with MD5, SHA-1, or RIPEMD authentication (RFC 2403/RFC 2404/RFC 2857); privacy is provided using DES-CBC encryption (RFC 2405), NULL encryption (RFC 2410), other CBC-mode algorithms (RFC 2451), or AES (RFC 3686). See also RFC 4305 and RFC 4308.

    0                   1                   2                   3
    0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ ----
   |               Security Parameters Index (SPI)                 | ^Int.
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ |Cov-
   |                      Sequence Number                          | |ered
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ | ----  
   |                    Payload Data* (variable)                   | |   ^
   ~                                                               ~ |   |
   |                                                               | |Conf.
   +               +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ |Cov-
   |               |     Padding (0-255 bytes)                     | |ered*
   +-+-+-+-+-+-+-+-+               +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ |   |
   |                               |  Pad Length   | Next Header   | v   v

   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ ------
   |         Integrity Check Value-ICV   (variable)                |
   ~                                                               ~
   |                                                               |

       * If included in the Payload field, cryptographic synchronization
         data, e.g., an Initialization Vector (IV), usually is not
         encrypted per se, although it often is referred to as being
         being part of the ciphertext.

FIGURE 13: IPsec Encapsulating Security Payload format. (From RFC 4303)

Figure 13 shows the format of the IPsec ESP information. Use of the IP ESP format is indicated by placing the value 50 (0x32) in the IPv4 Protocol or IPv6 Next Header field in the IP packet header. The ESP header (i.e., SPI and sequence number) follows mandatory IPv4/IPv6 header fields and precedes higher layer protocol (e.g., TCP, UDP) information. The contents of the ESP packet are:

Two types of SAs are defined in IPsec, regardless of whether AH or ESP is employed. A transport mode SA is a security association between two hosts. Transport mode provides the authentication and/or encryption service to the higher layer protocol. This mode of operation is only supported by IPsec hosts. A tunnel mode SA is a security association applied to an IP tunnel. In this mode, there is an "outer" IP header that specifies the IPsec destination and an "inner" IP header that specifies the destination for the IP packet. This mode of operation is supported by both hosts and security gateways.


   IPv4  |orig IP hdr  |     |      |
         |(any options)| TCP | Data |

   IPv6  |             | ext hdrs |     |      |
         | orig IP hdr |if present| TCP | Data |



    IPv4  |original IP hdr (any options) | AH | TCP |    Data   |
          |<- mutable field processing ->|<- immutable fields ->|
          |<----- authenticated except for mutable fields ----->|


   IPv6  |             |hop-by-hop, dest*, |    | dest |     |      |
         |orig IP hdr  |routing, fragment. | AH | opt* | TCP | Data |
         |<--- mutable field processing -->|<-- immutable fields -->|
         |<---- authenticated except for mutable fields ----------->|

               * = if present, could be before AH, after AH, or both


   IPv4 |                              |    | orig IP hdr*  |   |      |
        |new IP header * (any options) | AH | (any options) |TCP| Data |
        |<- mutable field processing ->|<------ immutable fields ----->|
        |<- authenticated except for mutable fields in the new IP hdr->|

   IPv6 |           | ext hdrs*|    |            | ext hdrs*|   |    |
        |new IP hdr*|if present| AH |orig IP hdr*|if present|TCP|Data|
        |<--- mutable field -->|<--------- immutable fields -------->|
        |       processing     |
        |<-- authenticated except for mutable fields in new IP hdr ->|

          * = if present, construction of outer IP hdr/extensions and
              modification of inner IP hdr/extensions is discussed in
              the Security Architecture document.

FIGURE 14: IPsec tunnel and transport modes for AH. (Adapted from RFC 4302)

Figure 14 show the IPv4 and IPv6 packet formats when using AH in both transport and tunnel modes. Initially, an IPv4 packet contains a normal IPv4 header (which may contain IP options), followed by the higher layer protocol header (e.g., TCP or UDP), followed by the higher layer data itself. An IPv6 packet is similar except that the packet starts with the mandatory IPv6 header followed by any IPv6 extension headers, and then followed by the higher layer data.

Note that in both transport and tunnel modes, the entire IP packet is covered by the authentication except for the mutable fields. A field is mutable if its value might change during transit in the network; IPv4 mutable fields include the fragment offset, time to live, and checksum fields. Note, in particular, that the address fields are not mutable.


      IPv4  |orig IP hdr  |     |      |
            |(any options)| TCP | Data |

      IPv6  |             | ext hdrs |     |      |
            | orig IP hdr |if present| TCP | Data |


      IPv4  |orig IP hdr  | ESP |     |      |   ESP   | ESP|
            |(any options)| Hdr | TCP | Data | Trailer | ICV|

                                |<---- encryption ---->|
                          |<-------- integrity ------->|

      IPv6  | orig |hop-by-hop,dest*,|   |dest|   |    | ESP   | ESP|

            |IP hdr|routing,fragment.|ESP|opt*|TCP|Data|Trailer| ICV|
                                         |<--- encryption ---->|
                                     |<------ integrity ------>|

                * = if present, could be before ESP, after ESP, or both


      IPv4  | new IP hdr+ |     | orig IP hdr+  |   |    | ESP   | ESP|
            |(any options)| ESP | (any options) |TCP|Data|Trailer| ICV|

                                |<--------- encryption --------->|
                          |<------------- integrity ------------>|

      IPv6  | new+ |new ext |   | orig+|orig ext |   |    | ESP   | ESP|
            |IP hdr| hdrs+  |ESP|IP hdr| hdrs+   |TCP|Data|Trailer| ICV|
                                |<--------- encryption ---------->|
                            |<------------ integrity ------------>|

            + = if present, construction of outer IP hdr/extensions and
                modification of inner IP hdr/extensions is discussed in
                the Security Architecture document.

FIGURE 15: IPsec tunnel and transport modes for ESP. (Adapted from RFC 4303)

Figure 15 shows the IPv4 and IPv6 packet formats when using ESP in both transport and tunnel modes.

Note a significant difference in the scope of ESP and AH. AH authenticates the entire packet transmitted on the network whereas ESP only covers a portion of the packet transmitted on the network (the higher layer data in transport mode and the entire original packet in tunnel mode). The reason for this is straight-forward; in AH, the authentication data for the transmission fits neatly into an additional header whereas ESP creates an entirely new packet which is the one encrypted and/or authenticated. But the ramifications are significant. ESP transport mode as well as AH in both modes protect the IP address fields of the original transmissions. Thus, using IPsec in conjunction with network address translation (NAT) might be problematic because NAT changes the values of these fields after IPsec processing.

The third component of IPsec is the establishment of security associations and key management. These tasks can be accomplished in one of two ways.

The simplest form of SA and key management is manual management. In this method, a security administer or other individual manually configures each system with the key and SA management data necessary for secure communication with other systems. Manual techniques are practical for small, reasonably static environments but they do not scale well.

For successful deployment of IPsec, however, a scalable, automated SA/key management scheme is necessary. Several protocols have defined for these functions:

On a final note, IPsec authentication for both AH and ESP uses a scheme called HMAC, a keyed-hashing message authentication code described in FIPS 198 and RFC 2104. HMAC uses a shared secret key between two parties rather than public key methods for message authentication. The generic HMAC procedure can be used with just about any hash algorithm, although IPsec specifies support for at least MD5 and SHA-1 because of their widespread use.

In HMAC, both parties share a secret key. The secret key will be employed with the hash algorithm in a way that provides mutual authentication without transmitting the key on the line. IPsec key management procedures will be used to manage key exchange between the two parties.

Recall that hash functions operate on a fixed-size block of input at one time; MD5 and SHA-1, for example, work on 64 byte blocks. These functions then generate a fixed-size hash value; MD5 and SHA-1, in particular, produce 16 byte (128 bit) and 20 byte (160 bit) output strings, respectively. For use with HMAC, the secret key (K) should be at least as long as the hash output.

The following steps provide a simplified, although reasonably accurate, description of how the HMAC scheme would work with a particular plaintext MESSAGE (Figure 16):

  1. Alice pads K so that it is as long as an input block; call this padded key Kp. Alice computes the hash of the padded key followed by the message, i.e., HASH (Kp:MESSAGE).
  2. Alice transmits MESSAGE and the hash value.
  3. Bob has also padded K to create Kp. He computes HASH (Kp:MESSAGE) on the incoming message.
  4. Bob compares the computed hash value with the received hash value. If they match, then the sender — Alice — must know the secret key and her identity is, thus, authenticated.

FIGURE 16: Keyed-hash MAC operation.

5.7. The SSL Family of Secure Transaction Protocols for the World Wide Web

The Secure Sockets Layer (SSL) protocol was developed by Netscape Communications to provide application-independent secure communication over the Internet for protocols such as the Hypertext Transfer Protocol (HTTP). SSL employs RSA and X.509 certificates during an initial handshake used to authenticate the server (client authentication is optional). The client and server then agree upon an encryption scheme. SSL v2.0 (1995), the first version publicly released, supported RC2 and RC4 with 40-bit keys. SSL v3.0 (1996) added support for DES, RC4 with a 128-bit key, and 3DES with a 168-bit key, all along with either MD5 or SHA-1 message hashes; this protocol is described in RFC 6101.

FIGURE 17: Browser encryption configuration screen (Firefox).

In 1997, SSL v3 was found to be breakable. By this time, the Internet Engineering Task Force (IETF) had already started work on a new, non-proprietary protocol called Transport Layer Security (TLS), described in RFC 2246 (1999). TLS extends SSL and supports additional crypto schemes, such as Diffie-Hellman key exchange and DSS digital signatures; RFC 4279 describes the pre-shared key crypto schemes supported by TLS. TLS is backward compatible with SSL (and, in fact, is recognized as SSL v3.1). SSL v3.0 and TLS v1.0 are the commonly supported versions on servers and browsers today (Figure 17); SSL v2.0 is rarely found today and, in fact, RFC 6176-compliant clients and servers that support TLS will never negotiate the use of SSL v2.

In 2002, a cipher block chaining (CBC) vulnerability was described for TLS v1.0. In 2011, the theoretical became practical when a CBC proof-of-concept exploit was released. Meanwhile, TLS v1.1 was defined in 2006 (RFC 4346), adding protection against v1.0's CBC vulnerability. In 2008, TLS v1.2 was defined (RFC 5246), adding several additional cryptographic options. Today, users are urged to use TLS v1.2 or v1.1 in lieu of any earlier versions, and v1.3 is available in draft form.

                       CLIENT       SERVER
 (using URL of form https://)       (listening on port 443) 

                  ClientHello ---->

                              <---- ServerHelloDone


                     Finished ---->

                              <---- Finished

             Application Data <---> Application Data

* Optional or situation-dependent messages; not always sent

FIGURE 18: SSL/TLS protocol handshake. (Adapted from RFC 2246)

Figure 18 shows the basic TLS (and SSL) message exchanges:

  1. URLs specifying the protocol https:// are directed to HTTP servers secured using SSL/TLS. The client will automatically try to make a TCP connection to the server at port 443. The client initiates the secure connection by sending a ClientHello message containing a Session identifier, highest SSL version number supported by the client, and lists of supported crypto and compression schemes (in preference order).
  2. The server examines the Session ID and if it is still in the server's cache, it will attempt to re-establish a previous session with this client. If the Session ID is not recognized, the server will continue with the handshake to establish a secure session by responding with a ServerHello message. The ServerHello repeats the Session ID, indicates the SSL version to use for this connection (which will be the highest SSL version supported by the server and client), and specifies which encryption method and compression method to be used for this connection.
  3. There are a number of other optional messages that the server might send, including:
    • Certificate, which carries the server's X.509 public key certificate (and, generally, the server's public key). This message will always be sent unless the client and server have already agreed upon some form of anonymous key exchange. (This message is normally sent.)
    • ServerKeyExchange, which will carry a premaster secret when the server's Certificate message does not contain enough data for this purpose; used in some key exchange schemes.
    • CertificateRequest, used to request the client's certificate in those scenarios where client authentication is performed.
    • ServerHelloDone, indicating that the server has completed its portion of the key exchange handshake.
  4. The client now responds with a series of mandatory and optional messages:
    • Certificate, contains the client's public key certificate when it has been requested by the server.
    • ClientKeyExchange, which usually carries the secret key to be used with the secret key crypto scheme.
    • CertificateVerify, used to provide explicit verification of a client's certificate if the server is authenticating the client.
  5. TLS includes the change cipher spec protocol to indicate changes in the encryption method. This protocol contains a single message, ChangeCipherSpec, which is encrypted and compressed using the current (rather than the new) encryption and compression schemes. The ChangeCipherSpec message is sent by both client and server to notify the other station that all following information will employ the newly negotiated cipher spec and keys.
  6. The Finished message is sent after a ChangeCipherSpec message to confirm that the key exchange and authentication processes were successful.
  7. At this point, both client and server can exchange application data using the session encryption and compression schemes.

Side Note: It would probably be helpful to make some mention of SSL (or, more properly, TLS) as it is used today. Most of us have used SSL to engage in a secure, private transaction with some vendor. The steps are something like this. During the SSL exchange with the vendor's secure server, the server sends its certificate to our client software. The certificate includes the vendor's public key and a signature from the CA that issued the vendor's certificate. Our browser software is shipped with the major CAs' certificates which contains their public key; in that way we authenticate the server. Note that the server does not use a certificate to authenticate us! Instead, we are generally authenticated when we provide our credit card number; the server checks to see if the card purchase will be authorized by the credit card company and, if so, considers us valid and authenticated! While bidirectional authentication is certainly supported by SSL, this form of asymmetric authentication is more commonly employed today since most users don't have certificates.

Microsoft's Server Gated Cryptography (SGC) protocol is another, albeit now defunct, extension to SSL/TLS. For several decades, it has been illegal to generally export products from the U.S. that employed secret-key cryptography with keys longer than 40 bits. For that reason, SSL/TLS has an exportable version with weak (40-bit) keys and a domestic (North American) version with strong (128-bit) keys. Within the last several years, however, use of strong SKC has been approved for the worldwide financial community. SGC is an extension to SSL that allows financial institutions using Windows NT servers to employ strong cryptography. Both the client and server must implement SGC and the bank must have a valid SGC certificate. During the initial handshake, the server will indicate support of SGC and supply its SGC certificate; if the client wishes to use SGC and validates the server's SGC certificate, the session can employ 128-bit RC2, 128-bit RC4, 56-bit DES, or 168-bit 3DES. Microsoft supports SGC in the Windows 95/98/NT versions of Internet Explorer 4.0, Internet Information Server (IIS) 4.0, and Money 98.

As mentioned above, SSL was designed to provide application-independent transaction security for the Internet. Although the discussion above has focused on HTTP over SSL (https/TCP port 443), SSL is also applicable to:

Protocol   TCP Port Name/Number
File Transfer Protocol (FTP)   ftps-data/989 & ftps/990
Internet Message Access Protocol v4 (IMAP4)   imaps/993
Lightweight Directory Access Protocol (LDAP)   ldaps/636
Network News Transport Protocol (NNTP)   nntps/563
Post Office Protocol v3 (POP3)   pop3s/995
Telnet   telnets/992

TLS was originally designed to operate over TCP. The IETF developed the Datagram Transport Layer Security (DTLS) protocol, based upon TLS, to operate over UDP. DTLS v1.2 is described in RFC 6347. (DTLS v1.0 can be found in RFC 4347.) RFC 6655 describes a suite of AES in Counter with Cipher Block Chaining - Message Authentication Code (CBC-MAC) Mode (CCM) ciphers for use with TLS and DTLS. An interesting analysis of the TLS protocol can be found in the paper "Analysis and Processing of Cryptographic Protocols" by Cowie.

Vulnerabilities: A vulnerability in the OpenSSL Library was discovered in 2014. Known as Heartbleed, this vulnerability had apparently been introduced into OpenSSL in late 2011 with the introduction of a feature called heartbeat. Heartbleed exploited an implementation flaw in order to exfiltrate keying material from an SSL server (or some SSL clients, in what is known at reverse Heartbleed); the flaw allowed an attacker to grab 64 KB blocks from RAM. Heartbleed is known to only affect OpenSSL v1.0.1 through v1.0.1f; the exploit was patched in v1.0.1g. In addition, the OpenSSL 0.9.8 and 1.0.0 families are not vulnerable. Note also that Heartbleed affects some versions of the Android operating system, notably v4.1.0 and v4.1.1 (and some, possibly custom, implementations of v4.2.2). Note that Heartbleed did not exploit a flaw in the SSL protocol, but rather a flaw in the OpenSSL implementation.

But that wasn't the only problem with SSL. In October 2014, a new vulnerability was found called POODLE (Padding Oracle On Downgraded Legacy Encryption), a man-in-the-middle attack that exploited another SSL vulnerability that had unknowingly been in place for many years. Weeks later, an SSL vulnerability in the bash Unix command shell was discovered, aptly named Shellshock. (Here's a nice overview of the 2014 SSL problems!) In March 2015, the Bar Mitzvah Attack was exposed, exploiting a 13-year old vulnerability in the Rivest Cipher 4 (RC4) encryption algorithm. Then there was the FREAK (Factoring Attack on RSA-EXPORT Keys CVE-2015-0204) SSL/TLS Vulnerabilty that affected some SSL/TLS implementations, including Android OS and Chrome browser for OS X later that month.

In March 2016, the SSL DROWN (Decrypting RSA with Obsolete and Weakened eNcryption) attack was announced. DROWN works by exploiting the presence of SSLv2 to crack encrypted communications and steal information from Web servers, email servers, or VPN sessions. You might have read above that SSLv2 fell out of use by the early 2000s and was formally deprecated in 2011. This is true. But backward compatibility often causes old software to remain dormant and it seems that up to one-third of all HTTPS sites are vulnerable to DROWN because SSLv2 has not been removed or disabled.

5.8. Elliptic Curve Cryptography (ECC)

In general, public key cryptography systems use hard-to-solve problems as the basis of the algorithm. The most predominant algorithm today for public key cryptography is RSA, based on the prime factors of very large integers. While RSA can be successfully attacked, the mathematics of the algorithm have not been comprised, per se; instead, computational brute-force has broken the keys. The defense is "simple" — keep the size of the integer to be factored ahead of the computational curve!

In 1985, Elliptic Curve Cryptography (ECC) was proposed independently by cryptographers Victor Miller (IBM) and Neal Koblitz (University of Washington). ECC is based on the difficulty of solving the Elliptic Curve Discrete Logarithm Problem (ECDLP). Like the prime factorization problem, ECDLP is another "hard" problem that is deceptively simple to state: Given two points, P and Q, on an elliptic curve, find the integer n, if it exists, such that P = nQ.

Elliptic curves combine number theory and algebraic geometry. These curves can be defined over any field of numbers (i.e., real, integer, complex) although we generally see them used over finite fields for applications in cryptography. An elliptic curve consists of the set of real numbers (x,y) that satisfies the equation:

y2 = x3 + ax + b

The set of all of the solutions to the equation forms the elliptic curve. Changing a and b changes the shape of the curve, and small changes in these parameters can result in major changes in the set of (x,y) solutions.

FIGURE 19: Elliptic curve addition.

Figure 19 shows the addition of two points on an elliptic curve. Elliptic curves have the interesting property that adding two points on the elliptic curve yields a third point on the curve. Therefore, adding two points, P and Q, gets us to point R, also on the curve. Small changes in P or Q can cause a large change in the position of R.

So let's go back to the original problem statement from above. The point Q is calculated as a multiple of the starting point, P, or, Q = nP. An attacker might know P and Q but finding the integer, n, is a difficult problem to solve. Q (i.e., nP) is the public key and n is the private key.

ECC may be employed with many Internet standards, including CCITT X.509 certificates and certificate revocation lists (CRLs), Internet Key Exchange (IKE), Transport Layer Security (TLS), XML signatures, and applications or protocols based on the cryptographic message syntax (CMS). RFC 5639 proposes a set of elliptic curve domain parameters over finite prime fields for use in these cryptographic applications and RFC 6637 proposes additional elliptic curves for use with OpenPGP.

RSA had been the mainstay of PKC for over a quarter-century. ECC, however, is emerging as a replacement in some environments because it provides similar levels of security compared to RSA but with significantly reduced key sizes. NIST use the following table to demonstrate the key size relationship between ECC and RSA, and the appropriate choice of AES key size:

TABLE 4. ECC and RSA Key Comparison.
(Source: Certicom, NIST)
ECC Key Size RSA Key Size Key-Size
AES Key Size
163 1,024 1:6 n/a
256 3,072 1:12 128
384 7,680 1:20 192
512 15,360 1:30 256
Key sizes in bits.

Since the ECC key sizes are so much shorter than comparable RSA keys, the length of the public key and private key is much shorter in elliptic curve cryptosystems. This results into faster processing times, and lower demands on memory and bandwidth; some studies have found that ECC is faster than RSA for signing and decryption, but slower for signature verification and encryption.

ECC is particularly useful in applications where memory, bandwidth, and/or computational power is limited (e.g., a smartcard) and it is in this area that ECC use is expected to grow. A major champion of ECC today is Certicom; readers are urged to see their ECC tutorial.

5.9. The Advanced Encryption Standard (AES) and Rijndael

The search for a replacement to DES started in January 1997 when NIST announced that it was looking for an Advanced Encryption Standard. In September of that year, they put out a formal Call for Algorithms and in August 1998 announced that 15 candidate algorithms were being considered (Round 1). In April 1999, NIST announced that the 15 had been whittled down to five finalists (Round 2): MARS (multiplication, addition, rotation and substitution) from IBM; Ronald Rivest's RC6; Rijndael from a Belgian team; Serpent, developed jointly by a team from England, Israel, and Norway; and Twofish, developed by Bruce Schneier. In October 2000, NIST announced their selection: Rijndael.

The remarkable thing about this entire process has been the openness as well as the international nature of the "competition." NIST maintained an excellent Web site devoted to keeping the public fully informed, at, which is now available as an archive site. Their Overview of the AES Development Effort has full details of the process, algorithms, and comments so I will not repeat everything here.

In October 2000, NIST released the Report on the Development of the Advanced Encryption Standard (AES) that compared the five Round 2 algorithms in a number of categories. The table below summarizes the relative scores of the five schemes (1=low, 3=high):

Category MARS RC6 Rijndael Serpent Twofish
General security 3 2 2 3 3
Implementation of security 1 1 3 3 2
Software performance 2 2 3 1 1
Smart card performance 1 1 3 3 2
Hardware performance 1 2 3 3 2
Design features 2 1 2 1 3

With the report came the recommendation that Rijndael be named as the AES standard. In February 2001, NIST released the Draft Federal Information Processing Standard (FIPS) AES Specification for public review and comment. AES contains a subset of Rijndael's capabilities (e.g., AES only supports a 128-bit block size) and uses some slightly different nomenclature and terminology, but to understand one is to understand both. The 90-day comment period ended on May 29, 2001 and the U.S. Department of Commerce officially adopted AES in December 2001, published as FIPS PUB 197.

AES (Rijndael) Overview

Rijndael (pronounced as in "rain doll" or "rhine dahl") is a block cipher designed by Joan Daemen and Vincent Rijmen, both cryptographers in Belgium. Rijndael can operate over a variable-length block using variable-length keys; the specification submitted to NIST describes use of a 128-, 192-, or 256-bit key to encrypt data blocks that are 128, 192, or 256 bits long; note that all nine combinations of key length and block length are possible. The algorithm is written in such a way that block length and/or key length can easily be extended in multiples of 32 bits and it is specifically designed for efficient implementation in hardware or software on a range of processors. The design of Rijndael was strongly influenced by the block cipher called Square, also designed by Daemen and Rijmen. See

  • The Rijndael page for a lot more information.

    Rijndael is an iterated block cipher, meaning that the initial input block and cipher key undergoes multiple rounds of transformation before producing the output. Each intermediate cipher result is called a State.

    For ease of description, the block and cipher key are often represented as an array of columns where each array has 4 rows and each column represents a single byte (8 bits). The number of columns in an array representing the state or cipher key, then, can be calculated as the block or key length divided by 32 (32 bits = 4 bytes). An array representing a State will have Nb columns, where Nb values of 4, 6, and 8 correspond to a 128-, 192-, and 256-bit block, respectively. Similarly, an array representing a Cipher Key will have Nk columns, where Nk values of 4, 6, and 8 correspond to a 128-, 192-, and 256-bit key, respectively. An example of a 128-bit State (Nb=4) and 192-bit Cipher Key (Nk=6) is shown below:

    s0,0 s0,1 s0,2 s0,3
    s1,0 s1,1 s1,2 s1,3
    s2,0 s2,1 s2,2 s2,3
    s3,0 s3,1 s3,2 s3,3
    k0,0 k0,1 k0,2 k0,3 k0,4 k0,5
    k1,0 k1,1 k1,2 k1,3 k1,4 k1,5
    k2,0 k2,1 k2,2 k2,3 k2,4 k2,5
    k3,0 k3,1 k3,2 k3,3 k3,4 k3,5

    The number of transformation rounds (Nr) in Rijndael is a function of the block length and key length, and is given by the table below:

    No. of Rounds
    Block Size
    128 bits
    Nb = 4
    192 bits
    Nb = 6
    256 bits
    Nb = 8
    128 bits
    Nk = 4
    10 12 14
    192 bits
    Nk = 6
    12 12 14
    256 bits
    Nk = 8
    14 14 14

    Now, having said all of this, the AES version of Rijndael does not support all nine combinations of block and key lengths, but only the subset using a 128-bit block size. NIST calls these supported variants AES-128, AES-192, and AES-256 where the number refers to the key size. The Nb, Nk, and Nr values supported in AES are:

    Variant Nb Nk Nr
    AES-128 4 4 10
    AES-192 4 6 12
    AES-256 4 8 14

    The AES/Rijndael cipher itself has three operational stages:

    • AddRound Key transformation
    • Nr-1 Rounds comprising:
      • SubBytes transformation
      • ShiftRows transformation
      • MixColumns transformation
      • AddRoundKey transformation
    • A final Round comprising:
      • SubBytes transformation
      • ShiftRows transformation
      • AddRoundKey transformation

    The paragraphs below will describe the operations mentioned above. The nomenclature used below is taken from the AES specification although references to the Rijndael specification are made for completeness. The arrays s and s' refer to the State before and after a transformation, respectively (NOTE: The Rijndael specification uses the array nomenclature a and b to refer to the before and after States, respectively). The subscripts i and j are used to indicate byte locations within the State (or Cipher Key) array.

    The SubBytes transformation

    The substitute bytes (called ByteSub in Rijndael) transformation operates on each of the State bytes independently and changes the byte value. An S-box, or substitution table, controls the transformation. The characteristics of the S-box transformation as well as a compliant S-box table are provided in the AES specification; as an example, an input State byte value of 107 (0x6b) will be replaced with a 127 (0x7f) in the output State and an input value of 8 (0x08) would be replaced with a 48 (0x30).

    One way to think of the SubBytes transformation is that a given byte in State s is given a new value in State s' according to the S-box. The S-box, then, is a function on a byte in State s so that:

    s'i,j = S-box (si,j)

    The more general depiction of this transformation is shown by:

    s0,0 s0,1 s0,2 s0,3
    s1,0 s1,1 s1,2 s1,3
    s2,0 s2,1 s2,2 s2,3
    s3,0 s3,1 s3,2 s3,3
    s'0,0 s'0,1 s'0,2 s'0,3
    s'1,0 s'1,1 s'1,2 s'1,3
    s'2,0 s'2,1 s'2,2 s'2,3
    s'3,0 s'3,1 s'3,2 s'3,3

    The ShiftRows transformation

    The shift rows (called ShiftRow in Rijndael) transformation cyclically shifts the bytes in the bottom three rows of the State array. According to the more general Rijndael specification, rows 2, 3, and 4 are cyclically left-shifted by C1, C2, and C3 bytes, respectively, per the table below:

    Nb C1 C2 C3
    4 1 2 3
    6 1 2 3
    8 1 3 4

    The current version of AES, of course, only allows a block size of 128 bits (Nb = 4) so that C1=1, C2=2, and C3=3. The diagram below shows the effect of the ShiftRows transformation on State s:

    State s
    s0,0 s0,1 s0,2 s0,3
    s1,0 s1,1 s1,2 s1,3
    s2,0 s2,1 s2,2 s2,3
    s3,0 s3,1 s3,2 s3,3
    ----------- no shift -----------> 
    ----> left-shift by C1 (1) ----> 
    ----> left-shift by C2 (2) ----> 
    ----> left-shift by C3 (3) ----> 
    State s'
    s0,0 s0,1 s0,2 s0,3
    s1,1 s1,2 s1,3 s1,0
    s2,2 s2,3 s2,0 s2,1
    s3,3 s3,0 s3,1 s3,2

    The MixColumns transformation

    The mix columns (called MixColumn in Rijndael) transformation uses a mathematical function to transform the values of a given column within a State, acting on the four values at one time as if they represented a four-term polynomial. In essence, if you think of MixColumns as a function, this could be written:

    s'i,c = MixColumns (si,c)

    for 0 ≤ i ≤ 3 for some column, c. The column position doesn't change, merely the values within the column.

    Round Key generation and the AddRoundKey transformation

    The AES Cipher Key can be 128, 192, or 256 bits in length. The Cipher Key is used to derive a different key to be applied to the block during each round of the encryption operation. These keys are called the Round Keys and each will be the same length as the block, i.e., Nb 32-bit words (words will be denoted W).

    The AES specification defines a key schedule by which the original Cipher Key (of length Nk 32-bit words) is used to form an Expanded Key. The Expanded Key size is equal to the block size times the number of encryption rounds plus 1, which will provide Nr+1 different keys. (Note that there are Nr encipherment rounds but Nr+1 AddRoundKey transformations.)

    Consider that AES uses a 128-bit block and either 10, 12, or 14 iterative rounds depending upon key length. With a 128-bit key, for example, we would need 1408 bits of key material (128x11=1408), or an Expanded Key size of 44 32-bit words (44x32=1408). Similarly, a 192-bit key would require 1664 bits of key material (128x13), or 52 32-bit words, while a 256-bit key would require 1920 bits of key material (128x15), or 60 32-bit words. The key expansion mechanism, then, starts with the 128-, 192-, or 256-bit Cipher Key and produces a 1408-, 1664-, or 1920-bit Expanded Key, respectively. The original Cipher Key occupies the first portion of the Expanded Key and is used to produce the remaining new key material.

    The result is an Expanded Key that can be thought of and used as 11, 13, or 15 separate keys, each used for one AddRoundKey operation. These, then, are the Round Keys. The diagram below shows an example using a 192-bit Cipher Key (Nk=6), shown in magenta italics:

    Expanded Key: W0 W1 W2 W3 W4 W5 W6 W7 W8 W9 W10 W11 W12 W13 W14 W15 ... W44 W45 W46 W47 W48 W49 W50 W51
    Round keys: Round key 0 Round key 1 Round key 2 Round key 3 ... Round key 11 Round key 12

    The AddRoundKey (called Round Key addition in Rijndael) transformation merely applies each Round Key, in turn, to the State by a simple bit-wise exclusive OR operation. Recall that each Round Key is the same length as the block.


    Ok, I hope that you've enjoyed reading this as much as I've enjoyed writing it — and now let me guide you out of the microdetail! Recall from the beginning of the AES overview that the cipher itself comprises a number of rounds of just a few functions:

    • SubBytes takes the value of a word within a State and substitutes it with another value by a predefined S-box
    • ShiftRows circularly shifts each row in the State by some number of predefined bytes
    • MixColumns takes the value of a 4-word column within the State and changes the four values using a predefined mathematical function
    • AddRoundKey XORs a key that is the same length as the block, using an Expanded Key derived from the original Cipher Key

    Cipher (byte in[4*Nb], byte out[4*Nb], word w[Nb*(Nr+1)])
      byte state[4,Nb]
      state = in
      AddRoundKey(state, w)
      for round = 1 step 1 to Nr-1
        AddRoundKey(state, w+round*Nb)
      end for
      AddRoundKey(state, w+Nr*Nb)
      out = state

    FIGURE 20: AES pseudocode.

    As a last and final demonstration of the operation of AES, Figure 20 is a pseudocode listing for the operation of the AES cipher. In the code:

    • in[] and out[] are 16-byte arrays with the plaintext and cipher text, respectively. (According to the specification, both of these arrays are actually 4*Nb bytes in length but Nb=4 in AES.)
    • state[] is a 2-dimensional array containing bytes in 4 rows and 4 columns. (According to the specification, this arrays is 4 rows by Nb columns.)
    • w[] is an array containing the key material and is 4*(Nr+1) words in length. (Again, according to the specification, the multiplier is actually Nb.)
    • AddRoundKey(), SubBytes(), ShiftRows(), and MixColumns() are functions representing the individual transformations.

    5.10. Cisco's Stream Cipher

    Stream ciphers take advantage of the fact that:

    x XOR y XOR y = x

    One of the encryption schemes employed by Cisco routers to encrypt passwords is a stream cipher. It uses the following fixed keystream (thanks also to Jason Fossen for independently extending and confirming this string):


    When a password is to be encrypted, the password function chooses a number between 0 and 15, and that becomes the offset into the keystream. Password characters are then XORed byte-by-byte with the keystream according to:

    Ci = Pi XOR K(offset+i)

    where K is the keystream, P is the plaintext password, and C is the ciphertext password.

    Consider the following example. Suppose we have the password abcdefgh. Converting the ASCII characters yields the hex string 0x6162636465666768.

    The keystream characters and hex code that supports an offset from 0 to 15 bytes and a password length up to 24 bytes is:

      d s f d ; k f o A , . i y e w r k l d J K D H S U B s g v c a 6 9 8 3 4 n c x

    Let's say that the function decides upon a keystream offset of 6 bytes. We then start with byte 6 of the keystream (start counting the offset at 0) and XOR with the password:

    XOR 0x6162636465666768

    The password would now be displayed in the router configuration as:

    password 7 06070D22484B0F1E0D

    where the "7" indicates the encryption type, the leading "06" indicates the offset into the keystream, and the remaining bytes are the encrypted password characters.

    (Decryption is pretty trivial so that exercise is left to the reader. If you need some help with byte-wise XORing, see If you'd like some programs that do this, see

    5.11. TrueCrypt

    TrueCrypt is an open source, on-the-fly crypto system that can be used on devices supports by Linux, MacOS, and Windows. First released in 2004, TrueCrypt can be employed to encrypt a partition on a disk or an entire disk.

    On May 28, 2014, the Web site was suddenly taken down and redirected to the SourceForge page. Although this paper is intended as a crypto tutorial and not a news source about crypto controversy, the sudden withdrawal of TrueCrypt cannot go without notice. Readers interested in using TrueCrypt should know that the last stable release of the product is v7.1a (February 2012); v7.2, released on May 28, 2014, only decrypts TrueCrypt volumes, ostensibly so that users can migrate to another solution. The current TrueCrypt Web page — TCnext — is The TrueCrypt Wikipedia page and accompanying references have some good information about the "end" of TrueCrypt as we knew it.

    While there does not appear to be any rush to abandon TrueCrypt, it is also the case that you don't want to use old, unsupported software for too long. A replacement was announced almost immediately upon the demise of TrueCrypt: "TrueCrypt may live on after all as CipherShed." The CipherShed group never produced a product, however, and the CipherShed Web site no longer appeared to be operational sometime after October 2016. Another — working — fork of TrueCrypt is VeraCrypt, which is also open source, multi-platform, operationally identical to TrueCrypt, and compatible with TrueCrypt containers.

    One final editorial comment. TrueCrypt was not broken or otherwise compromised! It was withdrawn by its developers for reasons that have not yet been made public but there is no evidence to assume that TrueCrypt has been damaged in any way; on the contrary, two audits, completed in April 2014 and April 2015, found no evidence of backdoors or malicious code. See Steve Gibson's TrueCrypt: Final Release Repository page for more information!

    TrueCrypt uses a variety of encryption schemes, including AES, Serpent, and Twofish. A TrueCrypt volume is stored as a file that appears to be filled with random data, thus has no specific file signature. (It is true that a TrueCrypt container will pass a chi-square (Χ2) randomness test, but that is merely a general indicator of possibly encrypted content. An additional clue is that a TrueCrypt container will also appear on a disk as a file that is some increment of 512 bytes in size. While these indicators might raise a red flag, they don't rise to the level of clearly indentifying a TrueCrypt volume.)

    When a user creates a TrueCrypt volume, a number of parameters need to be defined, such as the size of the volume and the password. To access the volume, the TrueCrypt program is employed to find the TrueCrypt encrypted file, which is then mounted as a new drive on the host system.

    FIGURE 21: TrueCrypt screen shot (Windows).

    FIGURE 22: TrueCrypt screen shot (MacOS).

    Consider this example where an encrypted TrueCrypt volume is stored as a file named James on a thumb drive. On a Windows system, this thumb drive has been mounted as device E:. If one were to view the E: device, any number of files might be found. The TrueCrypt application is used to mount the TrueCrypt file; in this case, the user has chosen to mount the TrueCrypt volume as device K: (Figure 21). Alternatively, the thumb drive could be used with a Mac system, where it has been mounted as the /Volumes/JIMMY volume. TrueCrypt mounts the encrypted file, James, and it is now accessible to the system (Figure 22).

    FIGURE 23: TrueCrypt hidden encrypted volume within an encrypted volume.

    One of the most interesting — certainly one of the most controversial — features of TrueCrypt is called plausible deniability, protection in case a user is "compelled" to turn over the encrypted volume's password. When the user creates a TrueCrypt volume, he/she chooses whether to create a standard or hidden volume. A standard volume has a single password, while a hidden volume is created within a standard volume and uses a second password. As shown in Figure 23, the unallocated (free) space in a TrueCrypt volume is always filled with random data, thus it is impossible to differentiate a hidden encrypted volume from a standard volume's free space.

    To access the hidden volume, the file is mounted as shown above and the user enters the hidden volume's password. When under duress, the user would merely enter the password of the standard (i.e., non-hidden) TrueCrypt volume.

    More information about TrueCrypt can be found at the TCnext Web Site or in the TrueCrypt User's Guide (v7.1a).

    An active area of research in the digital forensics community is to find methods with which to detect hidden TrueCrypt volumes. Most of the methods do not detect the presence of a hidden volume, per se, but infer the presence by forensic remnants left over. As an example, both Mac and Windows system usually have a file or registry entry somewhere containing a cached list of the names of mounted volumes. This list would, naturally, include the name of TrueCrypt volumes, both standard and hidden. If the user gives a name to the hidden volume, it would appear in such a list. If an investigator were somehow able to determine that there were two TrueCrypt volume names but only one TrueCrypt device, the inference would be that there was a hidden volume. A good summary paper that also describes ways to infer the presence of hidden volumes — at least on some Windows systems — can be found in "Detecting Hidden Encrypted Volumes" (Hargreaves & Chivers).

    Having nothing to do with TrueCrypt, but having something to do with plausible deniability and devious crypto schemes, is a new approach to holding password cracking at bay dubbed Honey Encryption. With most of today's crypto systems, decrypting with a wrong key produces digital gibberish while a correct key produces something recognizable, making it easy to know when a correct key has been found. Honey Encryption produces fake data that resembles real data for every key that is attempted, making it significantly harder for an attacker to determine whether they have the correct key or not; thus, if an attacker has a credit card file and tries thousands of keys to crack it, they will obtain thousands of possibly legitimate credit card numbers. See "'Honey Encryption' Will Bamboozle Attackers with Fake Secrets" (Simonite) for some general information or "Honey Encryption: Security Beyond the Brute-Force Bound" (Juels & Ristenpart) for a detailed paper.

    5.12. Encrypting File System (EFS)

    Microsoft introduced the Encrypting File System (EFS) into the NTFS v3.0 file system and has supported EFS since Windows 2000 and XP (although EFS is not supported in all variations of all Windows OSes). EFS can be used to encrypt individual files, directories, or entire volumes. While off by default, EFS encryption can be easily enabled via File Explorer (aka Windows Explorer) by right-clicking on the file, directory, or volume to be encrypted, selecting Properties, Advanced, and Encrypt contents to secure data (Figure 24). Note that encrypted files and directories are displayed in green in Windows Explorer.

    FIGURE 24: EFS and Windows (File) Explorer.

    The Windows command prompt provides an easy tool with which to detect EFS-encrypted files on a disk. The cipher command has a number of options, but the /u/n switches can be used to list all encrypted files on a drive (Figure 25).

    FIGURE 25: The cipher command.

    EFS supports a variety of secret key encryption schemes, including DES, DESX, and AES, as well as RSA public key encryption. The operation of EFS — at least at the theoretical level — is clever and simple.

    When a file is saved to disk:

    • A random File Encryption Key (FEK) is generated by the operating system.
    • The file contents are encrypted using one of the SKC schemes and the FEK.
    • The FEK is stored with the file, encrypted with the user's RSA public key. In addition, the FEK is encrypted with the RSA public key of any other authorized users and, optionally, a recovery agent's RSA public key.

    When the file is opened:

    • The FEK is recovered using the RSA private key of the user, other authorized user, or the recovery agent.
    • The FEK is used to decrypt the file's contents.

    There are weaknesses with the system, most of which are related to key management. As an example, the RSA private key can be stored on an external device such as a floppy disk (yes, really!), thumb drive, or smart card. In practice, however, this is rarely done; the user's private RSA key is often stored on the hard drive. In addition, early EFS implementations (prior to Windows XP SP2) tied the key to the username; later implementations employ the user's password.

    A more serious implementation issue is that a backup file named esf0.tmp is created prior to a file being encrypted. After the encryption operation, the backup file is deleted — not wiped — leaving an unencrypted version of the file available to be undeleted. For this reason, it is best to use encrypted directories because the temporary backup file is protected by being in an encrypted directory.

    FIGURE 26: EFS key storage. (Source:

    The EFS information is stored as a named stream in the $LOGGED_UTILITY_STREAM Attribute (attribute type 256 [0x100]). This information includes (Figure 26):

    • A Data Decryption Field (DDF) for every user authorized to decrypt the file, containing the user's Security Identifier (SID), the FEK encrypted with the user's RSA public key, and other information.
    • A Data Recovery Field (DRF) with the encrypted FEK for every method of data recovery

    Files in an NTFS file system maintain a number of attributes that contain the system metadata (e.g., the $STANDARD_INFORMATION attribute maintains the file timestamps and the $FILE_NAME attribute contains the file name). Files encrypted with EFS store the keys, as stated above, in a data stream named $EFS within the $LOGGED_UTILITY_STREAM attribute. Figure 27 shows the partial contents of the Master File Table (MFT) attributes for an EFS encrypted file.

    Master File Table (MFT) Parser V1.4 - Gary C. Kessler (7 June 2012)
    0056-0059  Attribute type: 0x10-00-00-00 [$STANDARD_INFORMATION]
    0060-0063  Attribute length: 0x60-00-00-00 [96 bytes]
    0064       Non-resident flag: 0x00 [Attribute is resident]
    0152-0155  Attribute type: 0x30-00-00-00 [$FILE_NAME]
    0156-0159  Attribute length: 0x78-00-00-00 [120 bytes]
    0160       Non-resident flag: 0x00 [Attribute is resident]
    0392-0395  Attribute type: 0x40-00-00-00 [$VOLUME_VERSION/$OBJECT_ID]
    0396-0399  Attribute length: 0x28-00-00-00 [40 bytes]
    0400       Non-resident flag: 0x00 [Attribute is resident]
    0432-0435  Attribute type: 0x80-00-00-00 [$DATA]
    0436-0439  Attribute length: 0x48-00-00-00 [72 bytes]
    0440       Non-resident flag: 0x01 [Attribute is non-resident]
    0504-0507  Attribute type: 0x00-01-00-00 [$LOGGED_UTILITY_STREAM]
    0508-0511  Attribute length: 0x50-00-2E-00 [80 bytes (ignore two high-order bytes)]
    0512       Non-resident flag: 0x01 [Attribute is non-resident]
    0568-0575  Name: 0x24-00-45-00-46-00-53-00 [$EFS]


    5.13. Some of the Finer Details of RC4

    RC4 is a variable key-sized stream cipher developed by Ron Rivest in 1987. RC4 works in output-feedback (OFB) mode, so that the key stream is independent of the plaintext. The algorithm is described in detail in Schneier's Applied Cryptography, 2/e, pp. 397-398 and the Wikipedia RC4 article.

    RC4 employs an 8x8 substitution box (S-box). The S-box is initialized so that S[i] = i, for i=(0,255).

    A permutation of the S-box is then performed as a function of the key. The K array is a 256-byte structure that holds the key (possibly supplemented by an Initialization Vector), repeating itself as necessary so as to be 256 bytes in length (obviously, a longer key results in less repetition). [[NOTE: All arithmetic below is assumed to be on a per-byte basis and so is implied to be modulo 256.]]

       j = 0
       for i = 0 to 255
         j = j + S[i] + K[i]
         swap (S[i], S[j])

    Encryption and decryption are performed by XORing a byte of plaintext/ciphertext with a random byte from the S-box in order to produce the ciphertext/plaintext, as follows:

       Initialize i and j to zero

    For each byte of plaintext (or ciphertext):

       i = i + 1
       j = j + S[i]
       swap (S[i], S[j])
       z = S[i] + S[j]

       Decryption: plaintext [i] = S[z] XOR ciphertext [i]
       Encryption: ciphertext [i] = S[z] XOR plaintext [i]

    A Perl implementation of RC4 (fine for academic, but not production, purposes) can be found at This program is an implementation of the CipherSaber version of RC4, which employs an initialization vector (IV). The CipherSaber IV is a 10-byte sequence of random numbers between the value of 0-255. The IV is placed in the first 10-bytes of the encrypted file and is appended to the user-supplied key (which, in turn, can only be up to 246 bytes in length).

    In 2014, Rivest and Schuldt developed a redesign of RC4 called Spritz. The main operation of Spritz is similar to the main operation of RC4, except that a new variable, w, is added:

       i = i + w
       j = k + S [j + S[i]]
       k = i + k + S[j]
       swap (S[i], S[j])
       z = (S[j + S[i + S[z+k]]]

       Decryption: plaintext [i] = S[z] XOR ciphertext [i]
       Encryption: ciphertext [i] = S[z] XOR plaintext [i]

    As seen above, RC4 has two pointers into the S-box, namely, i and j; Spritz adds a third pointer, k.

    Pointer i move slowly through the S-box; note that it is incremented by 1 in RC4 and by a constant, w, in Spritz. Spritz allows w to take on any odd value, ensuring that it is always relatively prime to 256. (In essence, RC4 sets w to a value of 1.)

    The other pointer(s) — j in RC4 or j and k in Spritz — move pseudorandomly through the S-box. Both ciphers have a single swap of entries in the S-box. Both also produce an output byte, z, as a function of the other parameters. Spritz, additionally, includes the previous value of z as part of the calculation of the new value of z.

    5.14. Challenge-Handshake Authentication Protocol (CHAP)

    CHAP, originally described in RFC 1994, and its variants (e.g., Microsoft's MS-CHAP) are authentication schemes that allow two parties to demonstrate knowledge of a shared secret without actually divulging that shared secret to a third party who might be eavesdropping.

    FIGURE 28: CHAP Handshake.

    The operation of CHAP is relatively straight-forward (Figure 28). Assume that the Client is logging on to a remote Server across the Internet. The Client needs to prove to the Server that it knows the password but doesn't want to reveal the password in any form that an eavesdropper can decrypt. In CHAP:

    1. The User sends the password (in plaintext) to the Server.
    2. The Server sends some random challenge string (i.e., some number of octets) to the User.
    3. Based upon the password and some algorithm, the User generates an encrypted response string (the same length as the challenge) and sends it to the Server.
    4. The Server looks up the User's password in it's database and, using the same algorithm, generates an expected response string.
    5. The Server compares its expected response to the actual response sent by the User. If the two match, the User is authenticated.

    Since the password is never revealed to a third-party, why can't we then just keep the same password forever? Note that CHAP is potentially vulnerable to a known plaintext attack; the challenge is plaintext and the response is encrypted using the password and a known CHAP algorithm. If an eavesdropper has enough challenge/response pairs, they might well be able to determine the password. Some other issues related to this form of authentication can be found in "Off-Path Hacking: The Illusion of Challenge-Response Authentication" (Gilad, Y., Herzberg, A., & Shulman, H., September-October 2014, IEEE Security & Privacy, 12(5), 68-77).

    5.15. Secure E-mail and S/MIME

    Electronic mail and messaging are the primary applications for which people use the Internet. Obviously, we want our e-mail to be secure; but, what exactly does that mean? And, how do we accomplish this task?

    There are a variety of ways to implement or access secure e-mail and cryptography is an essential component to the security of electronic mail. And, the good news is that we have already described all of the essential elements in the sections above. From a practical perspective, secure e-mail means that once a sender sends an e-mail message, it can only be read by the intended recipient(s). That can only accomplished if the encryption is end-to-end; i.e., the message must be encrypted before leaving the sender's computer and cannot be decrypted until it arrives at the recipient's system. But in addition to privacy, we also need the e-mail system to provide authentication, non-repudiation, and message integrity — all functions that are provided by a combination of hash functions, secret key crypto, and public key crypto. Secure e-mail services or software, then, usually provide two functions, namely, message signing and message encryption. Encryption, obviously, provides the secrecy; signing provides the rest.

    Figure 4, above, shows how the three different types of crypto schemes work together. For purposes of e-mail, however, it is useful to independently examine the functions of signing and encryption, if for no other reason than while secure e-mail applications and services can certainly sign and encrypt a message, they may also have the ability to sign a message without encrypting it or encrypt a message without signing it.

    FIGURE 29: Signing (top) and verifying (bottom) e-mail. (Source:

    E-mail messages are signed for the purpose of authenticating the sender, providing a mechanism so that the sender cannot later disavow the message (i.e., non-repudiation), and proving message integrity — unless, of course, the sender claims that their key has been stolen. The steps of signing and verifying e-mail are shown in Figure 29. To sign a message:

    1. The sender's software examines the message body.
    2. Information about the sender is retrieved (e.g., the sender's private key).
    3. The signing operation (e.g., encrypting the hash of the message with the sender's private key) is performed.
    4. The Digital Signature is appended to the e-mail message.
    5. The signed e-mail message is sent.

    Verification of the signed message requires the receiver's software to perform the opposite steps as the sender's software. In short, the receiver extracts the sender's Digital Signature, calculates a digital signature based upon the sender's information (e.g., using the sender's public key), and compares the computed signature with the received signature; if they match, the message's signature is verified. Note that if there are multiple recipients of the message, each will perform the same steps to verify the signature because the verification is base upon the sender's information (compare this to decryption, described below).

    FIGURE 30: Encrypting (top) and decrypting (bottom) e-mail. (Source:

    E-mail messages are encrypted for the purpose of privacy, secrecy, confidentiality — whatever term you wish to use to indicate that the message is supposed to be a secret between sender and receiver. The steps of encrypting and decrypting e-mail are shown in Figure 30. To encrypt a message:

    1. The sender's software examines the message body.
    2. The sender's software pulls out specific information about the recipient...
    3. ... and the encryption operation is performed.
    4. The encrypted message replaces the original plaintext e-mail message.
    5. The encrypted e-mail message is sent.

    Note that if the message has multiple recipients, the encryption step will yield different results because the encryption step is dependent upon the recipient's information (e.g., their public key). One application might choose to send a different encrypted message to each recipient; another might send the same encrypted message to each recipient, but encrypt the decryption key differently for each recipient (note further that this latter approach might allow a recipient to perform a known plaintext attack against the other recipients; each recipient knows the decryption key for the message and also sees the key encrypted with the recipient's information). In any case, recipient-specific information (e.g., their private key) must be used in order to decrypt the message and the decryption steps performed by the recipient are essentially the opposite of those performed by the sender.

    This discussion, so far, has been a little vague because different applications will act is different ways but, indeed, are performing very similar generic steps. There are two primary ways for a user to get send and receive secure e-mail, namely, to employ some sort of Web-based e-mail service or employ a secure e-mail client.

    If the reader is interested in using a Web-based secure e-mail service, you have only to do an Internet search to find many such services. All have slightly different twists to them, but here are a few representative free and commercial options:

    • 4SecureMail: Web-based e-mail service using 128-bit SSL between client and server; also supports many e-mail clients and mobile apps. Anonymous headers are "virtually untraceable." Non-4SecureMail recipients are notified by e-mail of waiting secure message which can be downloaded via browser; authenticity of the message is via the user's registered WaterMark (Figure 31).

    • CounterMail: Online, end-to-end e-mail service based upon OpenPGP. Multi-platform support, including Android. Has a USB key option, requiring use of a hardware dongle in order to retrieve mail.

    • Hushmail: Web- or client-based, end-to-end encrypted email based upon OpenPGP. Multi-platform support, including iPhone. Can send secure e-mail to non-Hushmail user by employing a shared password.

    • Kolab Now: Web-based secure e-mail service provider although it does not perform server-side e-mail encryption; they recommend that users employ a true end-to-end e-mail encryption solution. Data is stored on servers exclusively located in Switzerland and complies with the strict privacy laws of that country.

    • ProtonMail: End-to-end secure e-mail service using AES and OpenPGP, also located in Switzerland. Does not log users' IP addresses, thus provides an anonymous service. Multi-platform support, plus Android and iOS.

    • Tutanota: Web-, Android-, or iOS-based end-to-end secure e-mail service.

    FIGURE 31: E-mail message to non-4SecureMail user.

    The alternative to using a Web-based solution is to employ a secure e-mail client or, at least, a client that supports secure e-mail. Using host-based client software ensures end-to-end security — as long as the mechanisms are used correctly. There are no lack of clients that support secure mechanisms; Apple Mail, Microsoft Outlook, and Mozilla Thunderbird, for example, all have native support for S/MIME and have plug-ins that support OpenPGP/GPG (see Section 5.5 for additional information on the signing and encryption capabilities of PGP).

    The Secure Multipurpose Internet Mail Extensions (S/MIME) protocol is an IETF standard for use of public key-based encryption and signing of e-mail. S/MIME is actually a series of extensions to the MIME protocol, adding digital signature and encryption capability to MIME messages (which, in this context, refers to e-mail messages and attachments). S/MIME is based upon the original IETF MIME specifications and RSA's PKCS #7 secure message format, although it is now an IETF specification defined primarily in four RFCs:

    • RFC 3369: Cryptographic Message Syntax (CMS) (based upon PKCS #7) — Describes the syntax (format) used to digitally sign, digest, authenticate, or encrypt any type of message content, the rules for encapsulation, and an architecture for certificate-based key management.
    • RFC 3370: Cryptographic Message Syntax (CMS) Algorithms — Describes the use of common crypto algorithms to support the CMS, such as those for message digests (e.g., MD5 and SHA-1), signatures (e.g., DSA and RSA), key management, and content encryption (e.g., RC2 and 3DES).
    • RFC 3850: Secure/Multipurpose Internet Mail Extensions (S/MIME) Version 3.1 Certificate Handling — Specifies how S/MIME agents use the Internet X.509 Public Key Infrastructure (PKIX) and X.509 certificates to send and receive secure MIME messages. (See Section 4.3 for additional information about X.509 certificates.)
    • RFC 3851: Secure/Multipurpose Internet Mail Extensions (S/MIME) Version 3.1 Message Specification — Describes the "secure" part of the S/MIME protocol, add digital signature and encryption services to MIME. The MIME standard specifies the general structure for different content types within Internet messages; this RFC specifies cryptographically-enhanced MIME body parts.

    A quite good overview of the protocol can be found in a Microsoft TechNet article titled "Understanding S/MIME."

    Content-Type: multipart/signed;
       protocol="application/pkcs7-signature"; micalg=sha1
    Content-Transfer-Encoding: 7bit
    Content-Type: text/plain;
    Hi Carol.
    What was that pithy Groucho Marx quote?
    Content-Disposition: attachment;
    Content-Type: application/pkcs7-signature;
    Content-Transfer-Encoding: base64

    FIGURE 32: Sample multipart/signed message.

    Figure 32 shows a sample signed message using S/MIME. The first few lines indicate that this is a multipart signed message using the PKCS #7 signature protocol and, in this case, the SHA-1 hash. The two text lines following the first --Apple-Mail=... indicate that the message is in plaintext followed by the actual message. The next block indicates use of S/MIME where the signature block is in an attached file (the .p7s extension indicates that this is a signed-only message), encoded using BASE64.

    Content-Type: application/pkcs7-mime; name=smime.p7m; smime-type=enveloped-data
    Content-Transfer-Encoding: base64

    FIGURE 33: Sample S/MIME encrypted message.

    Figure 33 shows a sample encrypted message, carried as an S/MIME enveloped data attachment (.p7m) file, also formatted in BASE64. S/MIME can also attach certificate management messages (.p7c) and compressed data (.p7z). Many more S/MIME sample messages can be found in RFC 4134 ("Examples of S/MIME Messages").

    FIGURE 34: Sample S/MIME certificate.

    S/MIME is a powerful mechanism and is widely supported by many e-mail clients. To use your e-mail client's S/MIME functionality, you will need to have an S/MIME certificate (Figure 34). Several sites provide free S/MIME certificates for personal use, such as Instant SSL (Comodo), Secorio, and StartSSL (StartCom); commercial-grade S/MIME certificates are available from many other CAs. (NOTE: If these sites install your S/MIME certificate to your browser, you might need to export [backup] the certificate and import it so it can be seen by your e-mail application.)

    Do note that S/MIME is not necessarily well-suited for use with Web-based e-mail services. First off, S/MIME is designed for true end-to-end (i.e., client-to-client) encryption and Web mail services provide server-to-server or server-to-client encryption. Second, while S/MIME functionality could be built into browsers, the end-to-end security offered by S/MIME requires that the private key be accessible only to the end-user and not to the Web server. Finally, end-to-end encryption makes it impossible for a third-party to scan e-mail for viruses and other malware, thus obviating one of the advantages of using a Web-based e-mail service in the first place.


    This paper has briefly (!?) described how digital cryptography works. The reader must beware, however, that there are a number of ways to attack every one of these systems; cryptanalysis and attacks on cryptosystems, however, are well beyond the scope of this paper. In the words of Sherlock Holmes (ok, Arthur Conan Doyle, really), "What one man can invent, another can discover" ("The Adventure of the Dancing Men").

    There are a lot of topics that have been discussed above that will be big issues going forward in cryptography. As compute power increases, attackers can go after bigger keys and local devices can process more complex algorithms. Some of these issues include the size of public keys, the ability to forge public key certificates, which hash function(s) to use, and the trust that we will have in random number generators. Interested readers should check out "Recent Parables in Cryptography" (Orman, H., January/February 2014, IEEE Internet Computing, 18(1), 82-86).

    Cryptography is a particularly interesting field because of the amount of work that is, by necessity, done in secret. The irony is that secrecy is not the key to the goodness of a cryptographic algorithm. Regardless of the mathematical theory behind an algorithm, the best algorithms are those that are well-known and well-documented because they are also well-tested and well-studied! In fact, time is the only true test of good cryptography; any cryptographic scheme that stays in use year after year is most likely a good one. The strength of cryptography lies in the choice (and management) of the keys; longer keys will resist attack better than shorter keys.

    The corollary to this is that consumers should run, not walk, away from any product that uses a proprietary cryptography scheme, ostensibly because the algorithm's secrecy is an advantage. The observation that a cryptosystem should be secure even if everything about the system — except the key — is known by your adversary has been a fundamental tenet of cryptography for over 125 years. It was first stated by Dutch linguist Auguste Kerckhoffs von Nieuwenhoff in his 1883 (yes, 1883) papers titled La Cryptographie militaire, and has therefore become known as "Kerckhoffs' Principle."

    Getting a new crypto scheme accepted, marketed, and, commercially viable is a hard problem particularly if someone wants to make money off of the invention of a "new, unbreakable" methodology. Many people want to sell their new algorithm and, therefore, don't want to expose the scheme to the public for fear that their idea will be stolen. I observe that, consistent with Kerckhoffs' Principle, this approach is doomed to fail. A company won't invest in a secret scheme because there's no need; one has to demonstrate that their algorithm is better and stronger than what is currently available before someone else will invest time and money to explore an unknown promise. Regardless, I would also suggest that the way to make money in crypto is in the packaging — how does the algorithm fit into user applications and how easy is it for users to use? Check out a wonderful paper about crypto usability, titled "Why Johnny Can't Encrypt" (Whitten, A., & Tygar, J.D., 1999, Proceedings of the 8th USENIX Security Symposium, August 23-36, 1999, Washington, D.C., pp. 169-184.).

    As a slight aside, another way that people try to prove that their new crypto scheme is a good one without revealing the mathematics behind it is to provide a public challenge where the author encrypts a message and promises to pay a sum of money to the first person — if any — who cracks the message. Ostensibly, if the message is not decoded, then the algorithm must be unbreakable. As an example, back in ~2011, a $10,000 challenge page for a new crypto scheme called DioCipher was posted and scheduled to expire on 1 January 2013 — which it did. That was the last that I heard of DioCipher. I leave it to the reader to consider the validity and usefulness of the public challenge process.


    And for a purely enjoyable fiction book that combines cryptography and history, check out Neal Stephenson's Crytonomicon (published May 1999). You will also find in it a new secure crypto scheme based upon an ordinary deck of cards (ok, you need the jokers...) called the Solitaire Encryption Algorithm, developed by Bruce Schneier.

    Finally, I am not in the clothing business although I do have an impressive t-shirt collection (over 350 and counting!). I still proudly wear the DES (well, actually the IDEA) encryption algorithm t-shirt from 2600 Magazine which, sadly, appears to be no longer available (left). (It was always ironic to me that The Hacker Quarterly got the algorithm wrong but...) A t-shirt with Adam Back's RSA Perl code can be found at (right).


    A number of readers over time have asked for some rudimentary background on a few of the less well-known mathematical functions mentioned in this paper. Although this is purposely not a mathematical treatise, some of the math functions mentioned here are essential to grasping how modern crypto functions work. To that end, some of the mathematical functions mentioned in this paper are defined in greater detail below.

    A.1. The Exclusive-OR (XOR) Function

    Exclusive OR (XOR) is one of the fundamental mathematical operations used in cryptography (and many other applications). George Boole, a mathematician in the late 1800s, invented a new form of "algebra" that provides the basis for building electronic computers and microprocessor chips. Boole defined a bunch of primitive logical operations where there are one or two inputs and a single output depending upon the operation; the input and output are either TRUE or FALSE. The most elemental Boolean operations are:

    • NOT: The output value is the inverse of the input value (i.e., the output is TRUE if the input is false, FALSE if the input is true)
    • AND: The output is TRUE if all inputs are true, otherwise FALSE. (E.g., "the sky is blue AND the world is flat" is FALSE while "the sky is blue AND security is a process" is TRUE.)
    • OR: The output is TRUE if either or both inputs are true, otherwise FALSE. (E.g., "the sky is blue OR the world is flat" is TRUE and "the sky is blue OR security is a process" is TRUE.)
    • XOR (Exclusive OR): The output is TRUE if exactly one of the inputs is TRUE, otherwise FALSE. (E.g., "the sky is blue XOR the world is flat" is TRUE while "the sky is blue XOR security is a process" is FALSE.)

    I'll only discuss XOR for now and demonstrate its function by the use of a so-called truth tables. In computers, Boolean logic is implemented in logic gates; for design purposes, XOR has two inputs (black) and a single output (red), and its logic diagram looks like this:

    XOR Input #1
    0 1
    Input #2 0 0 1
    1 1 0

    So, in an XOR operation, the output will be a 1 if one input is a 1; otherwise, the output is 0. The real significance of this is to look at the "identity properties" of XOR. In particular, any value XORed with itself is 0 and any value XORed with 0 is just itself. Why does this matter? Well, if I take my plaintext and XOR it with a key, I get a jumble of bits. If I then take that jumble and XOR it with the same key, I return to the original plaintext.

    NOTE: Boolean truth tables usually show the inputs and output as a single bit because they are based on single bit inputs, namely, TRUE and FALSE. In addition, we tend to apply Boolean operations bit-by-bit. For convenience, I have created Boolean logic tables when operating on bytes.

    A.2. The modulo Function

    The modulo function is, simply, the remainder function. It is commonly used in programming and is critical to the operation of any mathematical function using digital computers.

    To calculate X modulo Y (usually written X mod Y), you merely determine the remainder after removing all multiples of Y from X. Clearly, the value X mod Y will be in the range from 0 to Y-1.

    Some examples should clear up any remaining confusion:

    • 15 mod 7 = 1
    • 25 mod 5 = 0
    • 33 mod 12 = 9
    • 203 mod 256 = 203

    Modulo arithmetic is useful in crypto because it allows us to set the size of an operation and be sure that we will never get numbers that are too large. This is an important consideration when using digital computers.

    A.3. Information Theory and Entropy

    Information theory is the formal study of reliable transmission of information in the least amount of space or, in the vernacular of information theory, the fewest symbols. For purposes of digital communication, a symbol can be a byte (i.e., an eight-bit octet) or an even smaller unit of transmission.

    The father of information theory is Bell Labs scientist and MIT professor Claude E. Shannon. His seminal paper, "A Mathematical Theory of Communication" (The Bell System Technical Journal, Vol. 27, pp. 379-423, 623-656, July, October, 1948), defined a field that has laid the mathematical foundation for so many things that we take for granted today, from data compression, data storage and communication, and quantum computing to language processing, plagiarism detection and other linguistic analysis, and statistical modeling. And, of course, cryptography — although crypto pre-dates information theory by nearly 2000 years.

    There are many everyday computer and communications applications that have been enabled by the formalization of information theory, such as:

    • Lossless data compression, where the compressed data is an exact replication of the uncompressed source (e.g., PKZip, GIF, PNG, and WAV).
    • Lossy data compression, where the compressed data can be used to reproduce the original uncompressed source within a certain threshold of accuracy (e.g., JPG and MP3).
    • Coding theory, which describes the impact of bandwidth and noise on the capacity of data communication channels from modems to Digital Subscriber Line (DSL) services, why a CD or DVD with scratches on the surface can still be read, and codes used in error-correcting memory chips and forward error-correcting satellite communication systems.

    One of the key concepts of information theory is that of entropy. In physics, entropy is a quantification of the disorder in a system; in information theory, entropy describes the uncertainty of a random variable or the randomness of an information symbol. As an example, consider a file that has been compressed using PKZip. The original file and the compressed file have the same information content but the smaller (i.e., compressed) file has more entropy because the content is stored in a smaller space (i.e., with fewer symbols) and each data unit has more randomness than in the uncompressed version. In fact, a perfect compression algorithm would result in compressed files with the maximum possible entropy; i.e., the files would contain the same number of 0s and 1s, and they would be distributed within the file in a totally unpredictable, random fashion.

    As another example, consider the entropy of passwords (this text is taken from my paper, "Passwords — Strengths And Weaknesses," citing an example from Firewalls and Internet Security: Repelling the Wily Hacker by Cheswick & Bellovin [1994]):

    Most Unix systems limit passwords to eight characters in length, or 64 bits. But Unix only uses the seven significant bits of each character as the encryption key, reducing the key size to 56 bits. But even this is not as good as it might appear because the 128 possible combinations of seven bits per character are not equally likely; users usually do not use control characters or non-alphanumeric characters in their passwords. In fact, most users only use lowercase letters in their passwords (and some password systems are case-insensitive, in any case). The bottom line is that ordinary English text of 8 letters has an information content of about 2.3 bits per letter, yielding an 18.4-bit key length for an 8-letter passwords composed of English words. Many people choose names as a password and this yields an even lower information content of about 7.8 bits for the entire 8-letter name. As phrases get longer, each letter only adds about 1.2 to 1.5 bits of information, meaning that a 16-letter password using words from an English phrase only yields a 19- to 24-bit key, not nearly what we might otherwise expect.

    Encrypted files tend to have a great deal of randomness. This is why a compressed file can be encrypted but an encrypted file cannot be compressed; compression algorithms rely on redundancy and repetitive patterns in the source file and such syndromes do not appear in encrypted files.

    Randomness is such an integral characteristic of encrypted files that an entropy test is often the basis for searching for encrypted files. Not all highly randomized files are encrypted, but the more random the contents of a file, the more likely that the file is encrypted. As an example, AccessData's Forensic Toolkit (FTK), software widely used in the computer forensics field, uses the following tests to detect encrypted files:

    • Arithmetic Mean: Calculated by summing all of the bytes in a file and dividing by the file length; if random, the value should be ~1.75.
    • Χ2 Error Percent: This distribution is calculated for a byte stream in a file; the value indicates how frequently a truly random number would exceed the calculated value.
    • Entropy: Describes the information density (per Shannon) of a file in bits/character; as entropy approaches 8, there is more randomness.
    • MCPI Error Percent: The Monte Carlo algorithm uses statistical techniques to approximate the value of π; a high error rate implies more randomness.
    • Serial Correlation Coefficient: Indicates the amount to which each byte is an e-mail relies on the previous byte. A value close to 0 indicates randomness.

    SIDEBAR: An 8-bit byte has 256 possible values. The entropy of a binary file can be calculated using the following formula:

    where n=256 and P(xi) is the probability of a byte in this file having the value i. A small Perl program to compute the entropy of a file can be found at

    Given this need for randomness, how do we ensure that crypto algorithms produce random numbers for high levels of entropy? Computers use random number generators (RNGs) for myriad purposes but computers cannot actually generate truly random sequences but, rather, sequences that have mostly random characteristics. To this end, computers use pseudorandom number generator (PRNG), aka deterministic random number generator, algorithms. NIST has a series of documents (SP 800-90: Random Bit Generators) that address this very issue:

    SIDEBAR: While the purpose of this document is to be tutorial in nature, I cannot totally ignore the disclosures of Edward Snowden in 2013 about NSA activities related to cryptography. One interesting set of disclosures is around deliberate weaknesses in the NIST PRNG standards at the behest of the NSA. NIST denies any such purposeful flaws but this will be evolving news over time. Interested readers might want to review "NSA encryption backdoor proof of concept published" (M. Lee) or "Dual_EC_DRBG backdoor: a proof of concept" (A. Adamantiadis).

    Along these lines, another perspective of the Snowden disclosures relates to the impact on the world's most confidential data and critical infrastructures if governments are able to access encrypted communications. In July 2015, 14 esteemed cryptographers and computer scientists released a paper continuing the debate around cryptography and privacy. The paper, titled "Keys Under Doormats: Mandating insecurity by requiring government access to all data and communications," argues that government access to individual users' encrypted information will ultimately yield significant flaws in larger systems and infrastructures. Also check out the N.Y. Times article, "Security Experts Oppose Government Access to Encrypted Communication" (N. Perlroth).

    For readers interested in learning more about information theory, see the following sites:

    Finally, it is important to note that information theory is an continually evolving field. There is an area of research essentially questioning the "power" of entropy in determining the strength of a cryptosystem. An interesting paper about this is "Brute force searching, the typical set and Guesswork" by Christiansen, Duffy, du Pin Calmon, & Médard (2013 IEEE International Symposium on Information Theory); a relatively non-technical overview of that paper can be found at "Encryption Not Backed by Math Anymore" by Hardesty (DFI News, 8/15/2013).

    A.4. Cryptography in the Pre-Computer Era

    This paper purposely focuses on cryptography terms, concepts, and schemes in current use and is not a treatise of the whole field. No mention is made here about pre-computerized crypto schemes, the difference between a substitution and transposition cipher, cryptanalysis, or other history, nor is there a lot of theory presented here. That said, the history and evolution of cryptography is really interesting and readers should check out some of the books in the References and Further Reading section below or some of the links in my crypto URLs page.

    There are also several excellent Web sites that provide detailed information about the history of cryptographic methods, such as:

    • Crypto Lab is a series of blog-like posts describing various encryption methods. The entire set of pages for offline viewing can be found at GitHub.

    • Crypto Programs is an online collection of more than 50 classical substitution and transposition encryption schemes.

    • The CrypTool Portal is designed to raise awareness about cryptography and contains a collection of free software with which to experiment with a variety of ciphers.

    • The Learn Cryptography Encryption page has a lot of information about classical and historic encryption methods, as well as pages about cryptanalysis, cryptocurrency, hash functions, and more.

    • The MultiWingSpan Ciphers page discusses a dozen or so manual encryption schemes as a setup to a series of programming assignments.

    • The Practical Cryptography Ciphers page provides history, math, and sample implementations of a couple dozen manual encryption codes. Other pages discuss cryptanalysis and hash functions.

    Finally, my software page contains a Perl program that implements several manual crypto schemes.


    Gary C. Kessler, Ph.D., CCE, CCFP, CISSP, is the president and janitor of Gary Kessler Associates, an independent consulting and training firm specializing in computer and network security, computer forensics, and TCP/IP networking. He has written over 75 papers, articles, and book chapters for industry publications, is co-author of ISDN, 4th. edition (McGraw-Hill, 1998), and is a past editor-in-chief of the Journal of Digital Forensics, Security and Law. Gary is also a Professor of Cybersecurity and chair of the Security Studies & International Affairs Dept. at Embry-Riddle Aeronautical University in Daytona Beach, Florida. He is a former-member of the Vermont Internet Crimes Against Children (ICAC) Task Force and currently works with the Hawaii and North Florida ICAC Task Forces, and is an Adjunct Professor at Edith Cowan University in Perth, Western Australia. Gary was formerly an Associate Professor and Program Director of the M.S. in Information Assurance program at Norwich University in Northfield, Vermont, and he started the M.S. in Digital Investigation Management and undergraduate Computer & Digital Forensics programs at Champlain College in Burlington, Vermont. Gary's e-mail address is and his PGP public key can be found at or on MIT's PGP keyserver (import the latest key!). Some of Gary's other crypto pointers of interest on the Web can be found at his Security-related URLs list. Gary is also a SCUBA instructor and U.S. Coast Guard licensed captain.


    This section was introduced late in the life of this paper and so I apologize to all of you who have made helpful comments that remain unacknowledged. If you did make comments that I adopted — from catching typographical or factual errors to suggesting a new resource or topic — and I have failed to recognize you, please remind me!

    Thanks are offered to Sitaram Chamarty, Bernhard Esslinger (and his students at the University of Siegen, Germany, contributors to the CrypTool project), William R. Godwin, Hugh Macdonald, and Douglas P. McNutt.