Cryptography is the art or science of secret writing, or more exactly, of storing information (for a shorter or longer period of time) in a form which allows it to be revealed to those you wish to see it yet hides it from all others. A cryptosystem is a method to accomplish this. Cryptanalysis is the practice of defeating such attempts to hide information. Cryptology includes both cryptography and cryptanalysis.

The original information to be hidden is called "plaintext". The hidden information is called "ciphertext". Encryption is any procedure to convert plaintext into ciphertext. Decryption is any procedure to convert ciphertext into plaintext.

A cryptosystem is designed so that decryption can be accomplished only under certain conditions, which generally means only by persons in possession of both a decryption engine (these days, generally a computer program) and a particular piece of information, called the decryption key, which is supplied to the decryption engine in the process of decryption.

Plaintext is converted into ciphertext by means of an encryption engine (again, generally a computer program) whose operation is fixed and determinate (the encryption method) but which functions in practice in a way dependent on a piece of information (the encryption key) which has a major effect on the output of the encryption process.

A cryptosystem could be designed which made use of several different methods of encryption, the particular method chosen for a particular encryption process being key-dependent. The combination of encryption methods results again in an encryption method, which is just as deterministic as a simpler cryptosystem, although probably harder for a cryptanalyst to crack. A good cryptosystem should in fact vary the details of its encryption method in a key-dependent way, though high security does not require the combination of distinct encryption algorithms.

The result of using the decryption method and the decryption key to decrypt ciphertext produced by using the encryption method and the encryption key should always be the same as the original plaintext (except perhaps for some insignificant differences).

In this process the encryption key and the decryption key may or may not be the same. When they are the cryptosystem is called a "symmetric key" system; when they are not it is called an "asymmetric key" system. The most widely-known instance of a symmetric cryptosystem is DES (the so-called "Data Encryption Standard"). The most widely-known instance of an asymmetric key cryptosystem is PGP ("Pretty Good Privacy").

An encryption algorithm (a precise specification of the steps to be taken when encrypting plaintext and when decrypting the resulting ciphertext) is known as an "asymmetric algorithm" if the encryption and decryption keys that it uses are different; otherwise it is a "symmetric algorithm".

There are many reasons for using encryption (examples are given below), and the cryptosystem that one should use is the one best suited for one's particular purpose and which satisfies the requirements of security, reliability and ease-of-use.

• Ease-of-use is easy to understand.
• Reliability means that the cryptosystem, when used as its designer intended it to be used, will always reveal exactly the information hidden when it is needed (in other words, that the ciphertext will always be recoverable and the recovered data will be the same as to the original plaintext).
• Security means that the cryptosystem will in fact keep the information hidden from all but those persons intended to see it despite the attempts of others to crack the system.

Ease-of-use is the quality easiest to ascertain. If the encryption key is a sequence of 64 hexadecimal digits (a 256-bit key), such as:

B923A24C98D98F83E24234CF8492C384E9AD19A128B3910F3904C324E920DA31

then you may have a problem not only in remembering it but also in using it (try typing the sequence above a few times). With such a key it is necessary to write it down or store it in a disk file, in which case there is the danger that it may be discovered by someone else. Thus such a key is not only inconvenient to use but also is a security risk.

A cryptosystem which is easy to use should allow keyboard entry of a string of from 10 to 60 characters, and thus a phrase which is easy to remember, e.g. "Lay on MacDuff!" Spaces should not be significant, and upper and lower case should be equivalent, so you don't have to be concerned about variants such as "Lay on Mac Duff!" or "Lay on Macduff!"

Reliability is the quality next easiest to test for. If it is not possible to provide a formal proof that the decryption of the encryption of the plaintext is always identical to the plaintext it is at least possible to write software to perform multiple encryptions and decryptions with many different keys to test for reliability (though this testing cannot be exhaustive). Such test software rarely accompanies commercial encryption software.

Finally there is the question of security. The security of a cryptosystem is always relative to the task it is intended to accomplish and the conditions under which it will be used. A theoretically secure system becomes insecure if used by people who write their encryption keys on pieces of paper which they stick to their computer terminals.

In general a cryptosystem can never be shown to be completely secure in practice, in the sense that without knowledge of the decryption key it is impossible to recover the plaintext with real-world computing power in less than, say, a thousand years. There is always something that could go wrong, and future advances in computing power (sufficient to render a cryptanalyst's task easy) cannot be known in advance.

In theory there is only one cryptosystem, a symmetric key system known as the "one-time pad", which is completely secure, but in practice it is cumbersome and the key can be used only once without compromising the security of the system. Because of its security, this is one of the methods used by governments to protect secrets, since they can afford the expense involved in dealing with the concomitant inconvenience.

In some cases it is possible to show that cracking a cryptosystem is equivalent to solving some particular mathematical problem, e.g. the problem of factoring large numbers ("large" here means numbers with several hundred decimal digits). If many mathematicians working for many years have been unable to solve a problem then this is a reason to regard a cryptosystem based on it as secure. However, there is no guarantee that a solution to the mathematical problem may not be found tomorrow, in which case the security of the cryptosystem would disappear overnight (or at least, as soon as word got around).

In the case of PGP and other encryption software such as RIPEM which rely on an asymmetric encryption algorithm known as the RSA Algorithm, it is widely believed that these are secure if and only if the problem of factoring large numbers is insoluble (that is, computationally infeasible in real time). In 1994 a claim was made by William H. Payne (but apparently not confirmed) that a method of cryptanalysis of the RSA Algorithm had been found which did not depend on a general solution to the problem of factoring large numbers. A poster to the Usenet newsgroup sci.crypt (Francis Barrett) remarked:

Although factoring is believed to be hard, and factoring breaks RSA, breaking RSA does not simplify factoring. Trivial non-factoring methods of breaking RSA could therefore exist. Whether this paper [by Payne] is legitimate remains to be seen, but it is certainly not beyond the realm of possiblity.

Some have claimed that PGP is the most secure encryption program available for PCs, a claim that does not withstand critical examination. Given two encryption programs, each of which generates random-looking ciphertext, how does one decide that one of them is "more secure" than the other -- even if full details of the encryption algorithms are known? Short of breaking one of the systems there is no clear answer. If one cannot provide criteria for determining when one program is more secure than another then it does not make sense to assert that one is the most secure.

A "brute force attack" upon a cryptosystem is one which involves trying every possible key to decrypt some ciphertext until finding one that works. Millions of keys are used in successive (or simultaneous) attempts to decrypt the ciphertext -- assuming the decryption method is known -- and the result in each case is tested to ascertain whether it is something intelligible (it is easy to distinguish text from random bytes).

Brute force attacks against specific cryptosystems can be compared since the average time required by a brute force attack is half the number of possible keys multiplied by the time required to test each key. It is true that if the size of the key space associated with a cryptosystem is small (e.g. 2^16 = 65,536) then the cryptosystem is vulnerable to a brute force attack. But if a cryptosystem has a very large key space (e.g. about 10^100 if a 60-character key is permitted) then a brute force attack is not feasible and so any weakness in the system, if it exists, must be sought elsewhere.

In practice, the security of a cryptosystem can only be measured by its resistance to actual attempts to break it. Those that have been broken are obviously insecure. (There are several commercially available PC encryption packages that have been broken; see for example the articles by Kochanski in the bibliography at the end of this article.) Those that have resisted the attentions of many cryptanalysts for many years may be deemed secure, at least until better methods of cryptanalysis are invented. All assertions that a new cryptosystem is weak are so much hot air unless a demonstration can be given that the system can be broken or unless specific theoretical weaknesses can be pointed out.

In the case of DES there has long been widespread suspicion that the National Security Agency (NSA) influenced its designers at IBM so that it was strong enough to withstand most attacks but not strong enough to withstand the NSA computers.

The original design submitted by IBM permitted all 16 x 48 = 768 bits of key used in the 16 rounds to be selected independently. A U.S. Senate Select Committee ascertained in 1977 that the U.S. National Security Agency (NSA) was instrumental in reducing the DES secret key to 56 bits that are each used many times, although this had previously been denied by IBM ... -- Massey, p.541.

But the best attempts by cryptanalysts over the years have produced only meager results (in particular, the demonstration of Adi Shamir that cryptanalysis of DES ciphertext, in the simplest DES mode (electronic code book), can be done with somewhat less effort than that required for a brute force attack). But recently a new method of DES cryptanalysis has been proposed which involves the use of parallel processing (using many computers simultaneously), and it now seems clear that for a few million dollars a computer can be built which can crack DES ciphertext in a few hours. Since NSA has practically unlimited funding and has the largest concentration of computing power and mathematical talent in the world, it is likely that NSA possesses the ability to decrypt DES ciphertext fairly easily.

In fact a brute force attack (using many computers working in parallel) has recently been used to break DES (though only in its simplest form -- so-called ECB mode).

NSA has, of course, never affirmed or denied their ability to crack DES. ("NSA" also is an acronym for "Never Say Anything" and -- in earlier years -- "No Such Agency".) However, the absence of publication of a demonstration that a particular cryptosystem has been cracked is no proof that it hasn't. Anyone who discovered a way to crack DES, RSA, etc., could make a lot more money by quietly providing a decryption service than by telling the world about his discovery. In fact if he did announce it people would quickly stop using that cryptosystem and he would have few clients.

When selecting a cryptosystem, or cryptographic software, you should first consider what you want it to accomplish. There are numerous (entirely law-abiding) reasons why you might wish to conceal information, for example:

1. Companies often possess data files on employees which are confidential, such as medical records, salary records, etc. Employees will feel safer knowing that these files are encrypted and are not accessible to casual inspection by data entry clerks (who may be bribed to obtain information on someone).
2. Individuals may share working space with others, of whose honor they are not entirely sure, and may wish to make certain that in their absence no-one will find anything by snooping about in their hard disk.
3. A company may wish to transfer sensitive business information between sites such as branch offices. Or it may wish to send confidential information (for example, a negotiating position, operating procedures or proprietary data) to an agent in the field (perhaps abroad). If the information is encrypted before transmission then one does not have to worry about it being intercepted since if this happens the encrypted data is incomprehensible (without the encryption key).
4. A company may have information that a competitor would like to see, such as information concerning legal or financial problems, results of research, who the customers are and what they are buying, information revealing violations of government regulations, secret formulas or details of manufacturing processes, plans for future expansion or for thedevelopment of new products.
5. A person or company may wish to transport to a distant location a computer which contains sensitive information without being concerned that if the computer is examined en route (e.g. by foreign customs agents) then the information will be revealed.
6. Two individuals may wish to correspond by email on matters that they wish to keep private and be sure that no-one else is reading their mail.

From the above examples it can be seen that there are two general cases when encryption is needed:

(a) When information, once encrypted, is simply to be stored on-site (and invulnerable to unauthorized access) until there is a need to access that information.

(b) When information is to be transmitted somewhere and it is encrypted so that if it is intercepted before reaching its intended destination the interceptor will not find anything they can make sense of.

In case (b) there arises the problem of secure key exchange. This problem exists because the person who will decrypt the information is usually not the same as the person who encrypted the information. Assuming that the decryptor is in posssession of the decryption engine (normally a piece of software) how does the decryptor know which decryption key to use? This information must be communicated to the decryptor in some way. If, during the course of this communication, the key is intercepted by a third party then that third party can intercept and decrypt the ciphertext subsequently sent by the encryptor to the decryptor.

This is a problem which all users of symmetric key systems, such as DES, must face when transmitting encrypted data, because in such systems the decryption key is the same as the encryption key. The encryptor can choose any encryption key they wish, but how are they to communicate that key to the decryptor in a secure way? Governments typically solve this problem by putting the key in a locked briefcase, handcuffing it to the wrist of a trusted minion, and despatching him with several armed guards to deliver the briefcase in person (typically at an embassy in a foreign country). This solution is generally too expensive for ordinary citizens.

If you know that your mail is not being opened then you can send the key that way, but who can be sure of this? Even registered mail may be opened. The best way to pass the key to whoever you will be sending encrypted material to is by personal contact someplace where there is no chance of being overheard. If this is not possible then various less secure means are available. For example, if you used to live in the same city as the person for some years then you might call them and say, "Remember that restaurant in San Diego where we used to have breakfast? Remember the name of that cute waitress?" Then you have a key that only you two know, unless someone has extensive information on your breakfast habits in San Diego several years ago and the names of the waitresses you might have come in contact with.

There is a class of cryptosystems knowns as "public key" systems which were first developed in the 1970s to solve this problem of secure key exchange. These are the systems referred to above as "asymmetric key" systems, in which the decryption key is not the same as the encryption key. Such public key systems can, if used properly, go a long way toward solving the problem of secure key exchange because the encryption key can be given out to the world without compromising the security of communication, provided that the decryption key is kept secret.

Let's say you wish to receive encrypted email from your girlfriend Alice. You send her your public key - the one used to perform encryption. Alice writes a passionate love letter, encrypts it with your public key and sends it to you. You decrypt it with your private key. If your other girlfriend Cheryl intercepts this then there is no way she can decrypt it because the public key (assumed to be known to everyone and thus to her) is no good for decryption. Decryption can only be performed with the private key, which only you know (unless Cheryl finds it on your PC when browsing through your files while you're taking a shower).

A public key cryptosystem relies on some mathematical procedure to generate the public and private keys. The mathematical nature of these systems usually allows the security of the system to be measured by the difficulty of solving some mathematical problem. There are several public key cryptosystems, the most well known being the one based on the RSA Algorithm (which is named after, and patented by, its inventors, Rivest, Shamir and Adelman), which, as noted above, relies for its security on the difficulty of factoring large numbers. There are two other public key systems available for licensing for commercial use, such as the LUC public key system (from LUC Encryption Technology, Sierra Madre, CA), and one developed by the computer manufacturer Next, Inc.

One should know that RSA is very vulnerable to chosen plaintext attacks. There is also a new timing attack that can be used to break many implementations of RSA. The RSA algorithm is believed to be safe when used properly, but one must be very careful when using it to avoid these attacks. -- Public Key Algorithms

Public key cryptography has applications beyond the classical one of hiding information. As a consequence of the encryption key and the decryption key being different, public key cryptography makes possible digital signatures (for authentification of documents) and digital forms of such activities as simultaneous contract signing. Digital cash is also an idea which builds on the use of an asymmetric cryptosystem.

Although public key cryptography in theory solves the problem of secure key exchange, it does in general have a couple of disadvantages compared to asymmetric (or secret) key systems. The first is speed. Generally public key systems, such as PGP, are much slower than secret key systems, and so may be suitable for encrypting small amounts of data, such as messages sent by email, but are not suitable for bulk encryption, where it may be required to encrypt megabytes of data. Secret key systems can be very fast (especially if implemented by instructions hard-coded into chips). The more complex such a system is the slower it tends to be, but even complex systems are generally of acceptable speed, especially given the developments in computer technology in recent years. A program that might have encrypted data at 4 KB/sec. in 1992 will soon (if not already) be able to encrypt at 100 Kb/sec.

The second disadvantage of public key systems is that there is a problem of key validation. If you wish to send encrypted data to a person, Fred, say, and you have obtained what is claimed to be Fred's public key, how do you know it really is Fred's public key? What if a third party, Louis, were to publish a public key in Fred's name? If Louis works for a government that likes to maintain a close watch over its citizens then perhaps he can monitor communications channels used by Fred, intercept encrypted data sent to him, and can then decrypt it (since he has the corresponding private key). If Louis were really cunning, and knew Fred's real public key, he could re-encrypt your message to Fred using the real public key (perhaps after altering your message in ways you might not approve of) and deliver it to Fred as if it had come directly from you. Fred would then decrypt it with his private key and read a message which he assumes is from you, but which may in fact be quite different from what you sent. In theory Louis could sit in the middle of an assumed two-way email correspondence between you and Fred, read everything each of you send to the other, and pass to each of you faked messages saying anything he wanted you to believe was from the other.

In 1993 a contributor to sci.crypt (Terry Ritter, 11/29/93) wrote:

When we have a secret-key cipher, we have the serious problem of transporting a key in absolute secrecy. However, after we do this, we can depend on the cipher providing its level of technical secrecy as long as the key is not exposed.

When we have a public-key cipher, we apparently have solved the problem of transporting a key. In fact, however, we have only done so if we ignore the security requirement to validate that key. Now, clearly, validation must be easier than secure transport, so it can be a big advantage. But validation is not trivial, and many people do not understand that it is necessary.

When we have a public-key cipher and use an unvalidated key, our messages could be exposed to a spoofer who has not had to "break" the cipher. The spoofer has not had to break RSA. The spoofer has not had to break IDEA. Thus, discussion of the technical strength of RSA and IDEA are insufficient to characterize the overall strength of such a cipher. In contrast, discussion of the technical strength of a secret-key cipher *IS* sufficient to characterize the strength of that cipher.

Discussion of the strength of public-key cipher mechanisms is irrelevant without a discussion of the strength of the public-key validation protocol. Private-key ciphers need no such protocol, nor any such discussion. And a public-key cipher which includes the required key-validation protocol can be almost as much trouble as a secret-key cipher which needs none.

When encryption is used in case (a), to be stored on-site (and invulnerable to unauthorized access) until there is a need to access that information, a secret key cryptosystem is clearly preferable, since such a system has the virtue of speed, and there is no problem of key validation and no problem of key exchange (since there is no need to transmit the encryption key to anyone other than by face-to-face communication).

However, many people are still using secret key cryptosystems that are relatively easy to break since those people don't know any better. For example, the WordPerfect word processing program allows you to lock the information in a file by means of a password. In a bad marriage one spouse might think that by locking their WordPerfect files they can write what they like and not worry that the other spouse might later use this against them. What the first spouse doesn't know is that there are programs around that can automatically (and in a few seconds) find the password used to lock a WordPerfect file.

In fact the WordPerfect encryption method (at least for Versions 5.1 and earlier) has been shown to be very easy to break. Full descriptions are given in the articles by Bennett, for Version 4.2, and by Bergen and Caelli, for Version 5.0 (see the bibliography below).

Another case is the encryption scheme used by Microsoft's word processing program Word. A method to crack encrypted Word files was published on Usenet late in 1993, so this method of protecting information is now obsolete. There is even a company, Access Data Recovery (in Orem, Utah) that sells software that automatically recovers the passwords used to encrypt data in a number of commercial software applications, including Lotus 123.

For a cryptosystem to be considered strong it should possess the following properties :

1. The security of a strong system resides with the secrecy of the key rather than with the supposed secrecy of the algorithm. In other words, even if an attacker knows the full details of the method used to encrypt and to decrypt, this should not allow him to decrypt the ciphertext if he does not know the key which was used to encrypt it (although obviously his task is even more difficult if he does not know the method -- and one might note that the Pentagon does not reveal details of its encryption techniques).
2. A strong cryptosystem has a large keyspace, that is, there are very many possible encryption keys. DES is considered by many to be flawed in this respect, because there are only 2^56 (about 10^17) possible keys. The size of the keyspace should be over 10^100, which is possible in systems which allow keys up to 60 characters in length (provided that no two keys are equivalent in their effect on the encryption process).
3. A strong cryptosystem will produce ciphertext which appears random to all standard statistical tests. A full discussion of these tests is beyond the scope of an introductory article such as this on the use of encryption software, but we may consider one interesting test, the so-called kappa test, otherwise known as the index of coincidence.

The idea behind this is as follows: Suppose that the elements of the cipher text are any of the 256 possible bytes (0 through FF). Consider the ciphertext to be a sequence of bytes (laid out in a row). Now duplicate this sequence and place it beneath the first (with the first byte of the second sequence below the first byte of the first sequence). We then have a sequence of pairs of identical bytes. Slide the lower sequence to the right a certain distance, say, 8 places. Then count how many pairs there are in which the bytes are identical. If the sequence of bytes were truly random then we would expect about 1/256 of the pairs to consist of identical bytes, i.e. about 0.39% of them. It is not difficult to write a program which analyzes a file of data, calculating the indices of coincidence (also known as the kappa value) for multiple displacement values.

When we run such a program on ordinary English text we obtain values such as the following ("IC" means "index of coincidence"):

 Offset IC coincidences1 5.85% 2397 in 409682 6.23% 2551 in 409673 9.23% 3780 in 409664 8.31% 3406 in 409655 7.91% 3240 in 409646 7.88% 3227 in 409637 7.78% 3187 in 409628 7.92% 3244 in 409619 8.24% 3377 in 4096010 7.98% 3268 in 4095911 8.16% 3341 in 4095812 8.09% 3315 in 4095713 8.15% 3337 in 4095614 7.97% 3264 in 4095515 7.97% 3265 in 4095416 8.07% 3306 in 4095317 8.04% 3293 in 4095218 7.85% 3214 in 40951

Typically only 80 or so different byte values occur in a file of English text. If these byte values occurred randomly then we would expect an index of coincidence for each displacement of about 1/80, i.e. about 1.25%. However, the distribution of characters in English text is not random ("e", "t" and the space character occur most frequently), which is why we obtain the larger IC values shown above.

The kappa test can be used to break a weak cryptosystem, or at least, to provide a clue toward breaking it. The index of coincidence for the displacement equal to the length of the encryption key will often be significantly higher than the other indices, in which case one can infer the length of the key.

For example, here are the indices of coincidence for a file of ciphertext (2048 bytes in size) produced by encrypting a text file using a weak cryptosystem (one which was discussed on sci.crypt in December 1993):

 Offset IC coincidences1 0.15% 3 in 20472 0.34% 7 in 20463 0.34% 7 in 20454 0.54% 11 in 20445 0.44% 9 in 20436 0.39% 8 in 20427 0.24% 5 in 20418 0.49% 10 in 20409 0.49% 10 in 203910 0.29% 6 in 203811 0.15% 3 in 203712 0.10% 2 in 203613 0.64% 13 in 203514 0.74% 15 in 203415 0.39% 8 in 203316 0.20% 4 in 203217 0.30% 6 in 203118 0.34% 7 in 2030

256 different byte values occur in the ciphertext, so if it were to appear as random then the kappa value should be about 0.39% for each displacement. But the kappa values for displacements 13 and 14 are significantly higher than the others, suggesting that the length of the key used in the encryption was either 13 or 14. This clue led to the decryption of the ciphertext and it turned out that the key length was in fact 13.

As an example of how non-random some ciphertext produced by commercial cryptosystems may be it is instructive to consider the proprietary encryption algorithm used by the Norton Diskreet program. The file named NORTON.INI, which comes with the Diskreet program, contains 530 bytes and 41 different byte values, including 403 instances of the byte value 0. The non-zero byte values are dispersed among the zero values. If we encrypt this file using Diskreet's proprietary encryption method and the key "ABCDEFGHIJ" we obtain a file, NORTON.SEC, which contains 2048 bytes, including 1015 0-bytes. When we examine this file with a hex editor we find that it consists of the letters "PNCICRYPT", seven 0-bytes or 1-bytes, 1024 bytes of apparent gibberish (the ciphertext) and finally 1008 0-bytes. Suppose we extract the 1024 bytes of ciphertext. There are 229 different byte values in this ciphertext, so if it really appeared random we would expect the kappa values to be about 1/229, i.e. about 0.44%. What we find is the following:

 Offset IC coincidences1 0.29% 3 in 10232 21.72% 222 in 10223 0.69% 7 in 10214 1.08% 11 in 10205 0.49% 5 in 10196 0.20% 2 in 10187 0.39% 4 in 10178 0.00% 0 in 10169 0.79% 8 in 101510 0.39% 4 in 101411 0.69% 7 in 101312 0.69% 7 in 101213 0.30% 3 in 101114 0.99% 10 in 101015 0.20% 2 in 100916 0.30% 3 in 100817 0.40% 4 in 100718 0.20% 2 in 1006

The figure of 21.72% for offset 2 is quite astounding. When we look at the ciphertext with a hex editor we see that there are many lines which have a byte pattern:

 xx yy aa bb aa bb cc dd cc dd ee ff ee ff gg hhgg hh ...

that is, in which pairs of bytes tend to be repeated, for example:

 4B 25 4B 25 8D 28 8D 28 2D F8 2D F8 21 AC21 AC E8 9E E8 9E F2 FC F2 FC C6 C5 C6 C5 7E 4F7E 4F B2 8B B2 8B 32 EE 32 EE 25 2C 25 2C A5 32A5 32 8D 61 8D 61 E5 C1 E5 C1 D4 F7 D4 F7

This explains why sliding the ciphertext against itself two places to the right produces such a large number of coincidences.

Clearly this ciphertext shows obvious regularities, and appears to be very far from random. Such regularities are what a cryptanalyst looks for, as a clue to the encryption method and to the key, and which a good cryptosystem denies him.

In contrast to Diskreet, a good cryptosystem would encrypt the same file, NORTON.INI, using the same key, to a file of a few hundred bytes with kappa values such as the following:

 Offset IC coincidences1 0.45% 2 in 4492 0.45% 2 in 4483 0.00% 0 in 4474 0.45% 2 in 4465 0.00% 0 in 4456 0.23% 1 in 4447 0.45% 2 in 4438 0.23% 1 in 4429 0.23% 1 in 44110 0.23% 1 in 44011 0.46% 2 in 43912 0.23% 1 in 43813 0.23% 1 in 43714 0.46% 2 in 43615 0.23% 1 in 43516 0.69% 3 in 43417 0.00% 0 in 43318 0.46% 2 in 432

The essentially discrete distribution of these indices of coincidence (0.00, 0.23, 0.46, 0.69) are due to the small size of the ciphertext (400 - 500 bytes). When the same test is done with about 60,000 bytes of ciphertext produced by a good cryptosystem (in which all 256 possible byte values should be present, implying a desired kappa value of 0.39%) we obtain a result such as:

 Offset IC coincidences1 0.41% 248 in 602002 0.43% 258 in 601993 0.44% 263 in 601984 0.43% 258 in 601975 0.43% 257 in 601966 0.34% 205 in 601957 0.40% 239 in 601948 0.42% 252 in 601939 0.40% 241 in 6019210 0.40% 242 in 6019111 0.41% 247 in 6019012 0.36% 216 in 6018913 0.41% 245 in 6018814 0.37% 223 in 6018715 0.36% 219 in 6018616 0.41% 247 in 6018517 0.40% 238 in 6018418 0.37% 222 in 60183

A good cryptosystem should produce ciphertext which passes the kappa test and other statistical tests and reveals no regularities or pattern of any kind.

Selected Bibliography

Cryptology is an academic discipline which has implications for the security of life and property, and thus there is a vast literature on the subject, often highly technical in nature. Much of the research is secret and unpublished. The following are just a few of the many books and journal articles available. The history of codes and code-breaking is especially interesting. The best book on this subject is David Kahn's The Codebreakers (the bound edition is recommended). Among the following works those marked with an asterisk are more historical than technical and tend to be somewhat easier reading. Those marked "#" contain commentary on some contemporary political aspects of the civilian use of cryptography.

Andreassen, K.: Computer Cryptology, Prentice-Hall.

Angluin, D. and Lichtenstein, D.: Provable Security in Cryptosystems, Yale University, 1983.

#Bamford, J.: The Puzzle Palace, Penguin Books.

#Barlow, J. P.: "Decrypting the Puzzle Palace", Communications of the ACM, July 1992, pp. 25-31.

*Barker, W. G.: History of Codes and Ciphers in the U.S., several volumes, Aegean Park Press, P. O. Box 2837, Laguna Hills, CA 92654.

Beker, H. and Piper, F.: Cipher Systems, Wiley, 1982.

Bennett, J.: "Analysis of the Encryption Algorithm Used in the WordPerfect Word Processing Program", Cryptologia 11(4), pp. 206-210, 1987.

Bergen, H. A. and Caelli, W. J.: "File Security in WordPerfect 5.0", Cryptologia 15(1), pp. 57-66, January 1991.

Biham, E. and Shamir, A.: "Differential cryptanalysis of DES-like cryptosystems", Journal of Cryptology, vol. 4, #1, pp. 3-72, 1991.

*Boyd, C.: "Anguish under Siege: High-Grade Japanese Signal Intelligence and the Fall of Berlin", Cryptologia 8(3), July 1989, pp. 193-209.

Brassard, G.: Modern Cryptology, Springer-Verlag, 1988.

Deavours, C. A. and Kruh, L.: Machine Cryptography and Modern Cryptanalysis, Artech House, 610 Washington St., Dedham, MA 02026, 1985.

DeLaurentis, J. M.: "A Further Weakness in the Common Modulus Protocol in the RSA Cryptoalgorithm", Cryptologia, 8(3), July 1984, pp. 253-259.

Denning, D.: Cryptography and Data Security, Addison-Wesley, 1982.

*Diffie, W.: "The first ten years of public key cryptography", IEEE proceedings, 76(5), 560--577, 1988.

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