Introduction to Cryptography

by Peter Meyer (Last revision 1994-04-29)

The purpose of this article is to provide information in the area of practical cryptography of interest to anyone wishing to use cryptographic software. I have mostly avoided discussion of technical matters in favor of a more general explanation of what I regard as the main things to be understood by someone beginning to use encryption. Those wishing to get more deeply into the theoretical aspects should consult Bruce Schneier's book (see bibliography at end).

Dolphin Software publishes several commercial cryptographic software products for the PC, including Dolphin Encrypt and Dolphin Encrypt Advanced Version (file and disk encryption software) and EZ-Crypt (an on-the-fly encryption TSR). (Product information available upon request). Occasionally in this article I include some remarks specifically concerning these or other products.

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 it 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.

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. Dolphin Encrypt and EZ-Crypt are symmetric key cryptosystems.

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:


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.

The key used in Dolphin Encrypt is any typeable string of from 10 to 60 characters and thus may be a phrase which is easy to remember, e.g. "Lay on MacDuff!" Spaces are not significant, and upper and lower case are equivalent, so you don't have to remember whether the key is "Lay on MacDuff!" 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 software is provided with Dolphin Encrypt.

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 one cryptosystem known as the one-time pad, which is absolutely secure, but in practice it is cumbersome and the key can be used only once without compromising the security of the system.

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). Yet recently a claim has been made, but has not been confirmed, that a method of cryptanalysis of the RSA Algorithm has been found which does not depend on a general solution to the problem of factor ing large numbers. A poster to the Usenet newsgroup sci.crypt (Francis Barrett) has 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 William H. 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 ask which is the most secure.

Brute force attacks upon a cryptosystem (a brute force attack involves trying every possible key to decrypt some ciphertext until finding one that works) 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 (by using it to decrypt the ciphertext and seeing whether anything intelligible results). 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 large key space (e.g. the key space associated with Dolphin Encrypt, whose size is about 10^109) then a brute force attack is not feasible and so any weakness in the system, if it exists, must be sought elsewhere.

Some may wonder: When trying to decrypt an encoded message by brute force, how does a computer know when it has succeeded? The answer is that in a brute force attack one tries one key after another, and if a key is incorrect the "decryption" will normally be garbage, i.e. will look like random bytes. There are statistical tests for randomness that can easily distinguish random bytes from natural language, so if the output does not appear like garbage then it is probably the plaintext, or at least is flagged for closer inspection. Randomness tests will distinguish between garbage and natural language text regardless of what the natural language is. More sensitive tests may actually be able to detect which natural language, since natural language texts in different languages have different statistical qualities.

In general, the security of a cryptosystem can only be measured by its resistance to actual attempts to break it in practice. 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.

In the case of DES there has long been widespread suspicion that the National Security Agency 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.

NSA has, of course, never affirmed or denied their ability to crack DES. (NSA also means Never Say Anything.) 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 (legitimate) reasons why you might wish to conceal information, for example:

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). 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. 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).

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 the development of new products. 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.

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 software program) 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 (e.g. DES and Dolphin Encrypt) 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 observed. 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? Let's use her name as the key." 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 call her and give 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 written on a piece of paper in the top drawer of the dresser under your socks).

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 numerous public key cryptosystems, the most well known being the one based on the RSA Algorithm (which is 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 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.

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 rather than running in a computer's memory). The more complex such a system is the slower it tends to be, but even complex systems are generally of acceptable speed. For example, Dolphin Encrypt will encrypt and decrypt at about 30 Kb/sec on a 80486 PC running at 50 Mhz (equivalent to 1 megabyte in 35 seconds), which is fast enough for most people.

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, Jack, were to publish a public key in Fred's name? If Jack works for a U.S. intelligence or law enforcement agency and can monitor communications channels used by Fred then he can intercept encrypted data sent to Fred, including any message you send to him, and can then decrypt it (since he has the corresponding private key). If Jack were really sneaky, 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 Jack 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.

A recent 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 (I shall illustrate these by reference to the Dolphin Encrypt file encryption software):

(i) 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). The encryption algorithm used in Dolphin Encrypt is defined by the C source code for the encryption and decryption functions, and this source code is part of a publicly available C function library (the Dolphin Encryption Library). The method is not secret and its full details are available for examination to anyone who purchases the library.

(ii) 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 associated with Dolphin Encrypt is about 10^109, due to the fact that keys can be up to 60 characters in length.

(iii) 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 coincidences

1 5.85% 2397 in 40968
2 6.23% 2551 in 40967
3 9.23% 3780 in 40966
4 8.31% 3406 in 40965
5 7.91% 3240 in 40964
6 7.88% 3227 in 40963
7 7.78% 3187 in 40962
8 7.92% 3244 in 40961
9 8.24% 3377 in 40960
10 7.98% 3268 in 40959
11 8.16% 3341 in 40958
12 8.09% 3315 in 40957
13 8.15% 3337 in 40956
14 7.97% 3264 in 40955
15 7.97% 3265 in 40954
16 8.07% 3306 in 40953
17 8.04% 3293 in 40952
18 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 coincidences 1 0.15% 3 in 2047 2 0.34% 7 in 2046 3 0.34% 7 in 2045 4 0.54% 11 in 2044 5 0.44% 9 in 2043 6 0.39% 8 in 2042 7 0.24% 5 in 2041 8 0.49% 10 in 2040 9 0.49% 10 in 2039 10 0.29% 6 in 2038 11 0.15% 3 in 2037 12 0.10% 2 in 2036 13 0.64% 13 in 2035 14 0.74% 15 in 2034 15 0.39% 8 in 2033 16 0.20% 4 in 2032 17 0.30% 6 in 2031 18 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 coincidences 1 0.29% 3 in 1023 2 21.72% 222 in 1022 3 0.69% 7 in 1021 4 1.08% 11 in 1020 5 0.49% 5 in 1019 6 0.20% 2 in 1018 7 0.39% 4 in 1017 8 0.00% 0 in 1016 9 0.79% 8 in 1015 10 0.39% 4 in 1014 11 0.69% 7 in 1013 12 0.69% 7 in 1012 13 0.30% 3 in 1011 14 0.99% 10 in 1010 15 0.20% 2 in 1009 16 0.30% 3 in 1008 17 0.40% 4 in 1007 18 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 hh gg 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 AC 21 AC E8 9E E8 9E F2 FC F2 FC C6 C5 C6 C5 7E 4F 7E 4F B2 8B B2 8B 32 EE 32 EE 25 2C 25 2C A5 32 A5 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, Dolphin Encrypt encrypts the same file, NORTON.INI, using the same key, to a file of 450 bytes (in which there are 207 different byte values, implying that the kappa values should be about 0.48% if the ciphertext is to appear random) with kappa values as follows:

Offset IC coincidences 1 0.45% 2 in 449 2 0.45% 2 in 448 3 0.00% 0 in 447 4 0.45% 2 in 446 5 0.00% 0 in 445 6 0.23% 1 in 444 7 0.45% 2 in 443 8 0.23% 1 in 442 9 0.23% 1 in 441 10 0.23% 1 in 440 11 0.46% 2 in 439 12 0.23% 1 in 438 13 0.23% 1 in 437 14 0.46% 2 in 436 15 0.23% 1 in 435 16 0.69% 3 in 434 17 0.00% 0 in 433 18 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 (450 bytes). When we do the same test for a file of Dolphin ciphertext of size 60201 bytes (in which there are 256 different byte values, implying a desired kappa value of 0.39%) we find:

Offset IC coincidences
1 0.41% 248 in 60200
2 0.43% 258 in 60199
3 0.44% 263 in 60198
4 0.43% 258 in 60197
5 0.43% 257 in 60196
6 0.34% 205 in 60195
7 0.40% 239 in 60194
8 0.42% 252 in 60193
9 0.40% 241 in 60192
10 0.40% 242 in 60191
11 0.41% 247 in 60190
12 0.36% 216 in 60189
13 0.41% 245 in 60188
14 0.37% 223 in 60187
15 0.36% 219 in 60186
16 0.41% 247 in 60185
17 0.40% 238 in 60184
18 0.37% 222 in 60183

The kappa test, and other statistical tests, reveal no regularities in the ciphertext produced by Dolpin Encrypt (or by EZ-Crypt).

When evaluating an encryption program it is reasonable to ask whether the cipher used is something as weak as a repeated exclusive-or cipher, in which the bytes of the key are repeatedly exclusive-or'd against those of the plaintext - the sort of "crypto system designed by a 16-year-old on a long weekend" that some like to accuse very new system of being. In a such a crypto system each byte of the ciphertext is affected only by the corresponding byte in the key and not by every byte (or every bit) in the key. In this case the system is generally easy to crack (by determining the length of the key, say n, and then considering the n sets of bytes affected by each byte in the ciphertext). Some simple tests of the encryption program may be performed to answer this question of the extent of the dependence of each byte of the ciphertext on all of, or only on some of, the bytes of the key. To illustrate in the case of Dolphin Encrypt:

A file, NULLFILE, of 50,000 zero-bytes (good for testing ciphers because the plaintext consists entirely of a single byte value) was encrypted using Dolphin Encrypt and two similar keys, "abcdefghij" and "abcdefghik". These keys differ only in their final bit ('k' instead of 'j'). The ciphertext files produced were, respectively, NULLFILE.E1 (length 1800 bytes) and NULLFILE.E2 (length 1830) bytes (Dolphin Encrypt performs compression before encryption). A byte-by-byte file comparison utility was run on the two output files, with the following result:

File 1: NULLFILE.E1 Filesize: 1800
File 2: NULLFILE.E2 Filesize: 1830

152 bytes are different. One byte is identical. 38 bytes are different. One byte is identical. 31 bytes are different. One byte is identical. 174 bytes are different. One byte is identical. 107 bytes are different. One byte is identical. 318 bytes are different. One byte is identical. 155 bytes are different. One byte is identical. 175 bytes are different. One byte is identical. 8 bytes are different. One byte is identical. 125 bytes are different. One byte is identical. 42 bytes are different. One byte is identical. 464 bytes are different.

Thus exactly 11 bytes, at apparently random locations, in the first 1800 bytes of the first file were the same as the bytes in the corresponding positions in the second file. This is more-or-less what we would expect when comparing files which consist of what appear to be random bytes and which are independent of each other (since 1800/256 = 7.03).

A similar test is to take a string of characters such as "aabbccddee" and encrypt it using two keys which differ by one bit. When this string is encrypted using Dolphin Encrypt and the keys "abcdefghij" and "abcdefghik" (as before) the resulting ciphertext is as follows (these are hexdumps of the two ciphertext files):

85 E0 08 22 F6 54 27 DE - 6A 1F A0 2C 8F C1 C7 D3 ...".T'.j..,.... 87 54 DF 59 CF 2F 75 64 - 82 D3 95 23 2A 70 3D EA .T.Y./ud...#*p=. D6 AB 12 1C 6D 9E 52 4E - 41 20 0A A9 E7 47 89 90 ....m.RNA ...G.. 47 2C 14 83 EF EE DB 44 - AD FA 2C 38 5C 89 E7 0F G,.....D..,8\... FE 6A EC 16 7C 55 33 EC - 51 2E 52 5C 30 9F 0B 00 .j..|U3.Q.R\0.. 7C 11 91 7B 25 B6 66 10 - 24 B4 29 E1 14 88 12 00 |..{%.f.$.).... 49 03 E5 6A 10 99 37 24 - 98 B9 28 I..j..7$..(

A2 59 8D 70 B3 B0 44 D1 - C9 F9 54 EE CA 2E 4D 7C .Y.p..D...T...M| FE 39 72 7B F3 C3 D6 87 - 64 EC 2A 5E AD ED D3 9D .9r{....d.*^.... 81 FC 40 CA DF 71 7A 97 - 42 26 FC 65 19 23 C6 08 ..@..qz.B&.e.#.. 76 7B AD CA 0A 71 F5 B2 - 51 DF 21 06 0A D9 0A 0E v{...q..Q.!..... EA 8D EA 14 88 C8 22 69 - B1 38 66 D1 89 DE 00 56 ......"i.8f... V 0A F7 F6 C4 E9 57 B7 92 - BF E5 1C 58 8B 14 2F B7 .....W.....X../. 01 2F 00 CF 5E 06 69 4D - AD 43 F9 DC 94 ./ .^.iM.C...

The ciphertext produced is quite different even though the keys are almost the same. In fact, each byte in the first ciphertext block is different from its corresponding byte in the second ciphertext block.

When attempting to break a cipher this test is often one of the first to be applied, namely, take some known plaintext and encrypt it with slightly different keys and compare the resulting ciphertext to see whether a particular change in the key produces a particular change in the ciphertext. With a strong cipher a change of a single bit in the key will have a cascading effect, producing large changes in the resulting ciphertext, as we see above.

As to the increase in size of the ciphertext in this case: Dolphin Encrypt adds random bytes (a.k.a. garbage) to the ciphertext (this makes crypt- analysis of the cipher more difficult), so very small files are increased. Larger ciphertext blocks (a few Kb or more) are usually considerably smaller than the plaintext blocks because the decrease in size resulting from compression is usually much more than the increase resulting from interpolation of random bytes.

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 Crypt- analysis, 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. ---- and Hellman, M.: "Privacy and authentication: an introduction to cryptography", IEEE proceedings, 67(3), 397-427, 1979. Feistel, H.: "Cryptography and Computer Privacy", Scientific American, 228(5), pp. 15-23, 1973. Flicke, W. F.: War Secrets in the Ether, Volumes 1 & 2, Aegean Park Press. Friedman, W. F.: Solving German Codes in World War I, Aegean Park Press. ---- and Mendelsohn, C. J.: The Zimmermann Telegram of 1917 and its Cryptographic Backround, Aegean Park Press. Gaines, H. F.: Cryptanalysis, Dover, 1956. Garon, G. and Outerbridge, R.: "DES watch: an examination of the sufficiency of the Data Encryption Standard for financial institutions in the 1990's", Cryptologia 15(3), 1991, pp. 177-193. Hinsley, F. H. et al.: British Intelligence in the Second World War, Cambridge U. P., volumes 1 - 4. ---- and Stripp, A. (eds.): Codebreakers: The Inside Story of Bletchley Park, Oxford U.P., 1993. Held, G.: Top Secret Data Encryption Techniques, Sams Publishing, 1993. Hellman, M.: "The mathematics of public key cryptography", Scientific American, pp. 130-139, 1979. Kahn, D.: The Codebreakers, Macmillan, 1967. ----: Seizing the Enigma, Houghton Mifflin, 1991. Kochanski, M.: "A Survey of Data Insecurity Packages", Cryptologia 11(1), pp. 1-15, 1987. ----: "Another Data Insecurity Package", Cryptologia 12(3), pp.165-177, July 1988. Konheim, A. G.: Cryptography: A Primer, John Wiley, 1981. #Kruh, L.: "The Control of Public Cryptography and Freedom of Speech - A Review", Cryptologia 10(1), January 1986, pp. 2-9. Lysing, H.: Secret Writing, Dover, 1974. Marotta, M.: The Code Book, Loompanics, 1987. Massey, J.: "An Introduction to Contemporary Cryptology", IEEE Proceedings, 76(5), pp. 533-549, May 1988. Meyer, C. H., and Matyas, S. M.: Cryptography, John Wiley, 1982. #Pierce, K. J.: "Public Cryptography, Arms Export Controls, and the First Amendment: A Need for Legislation", Cornell International Law Journal, Vol. 17, No. 3 (Winter 1984), pp. 197-236. Rivest, R. L., Shamir, A. and Adelman, L.: "A Method for Obtaining Digital Signatures and Public-key Cryptosystems," Communications of the ACM, February 1979. Salomaa, A.: Public Key Cryptography, Springer-Verlag, 1990. Schneier, B.: "Untangling Public Key Cryptography", Dr Dobb's Journal, May 1992, pp. 16-28. ----: "The IDEA Encryption Algorithm", Dr Dobb's Journal, December 1993, pp. 50-56. ----: Applied Cryptography, John Wiley & Sons, 1994. Simmons, G. (ed.): Contemporary Cryptology: the Science of Information Integrity, IEEE Press, 1991. Smith, L. D.: Cryptography, Dover, 1955. Weber, R. E.: United States Diplomatic Codes and Ciphers 1775-1938, Precedent, 1979. Welsh, D.: Codes and Cryptography, Claredon Press, 1988. Yardley, H. O.: The American Black Chamber, Ballantine 1981.