cryptography

Unbreakable ciphers

Unbreakable ciphers are possible. But the key must be randomly selected and used only once, and its length must be equal to or greater than that of the plaintext to be enciphered. Therefore such long keys, called one-time tapes, are not practical in data-processing applications. To work well, a key must be of fixed length, relatively short, and capable of being repeatedly used without compromising security. In theory, any algorithm that uses such a finite key can be analyzed; in practice, the effort and resources necessary to break the algorithm would be unjustified.

Strong algorithms

Fortunately, to achieve effective data security, construction of an unbreakable algorithm is not necessary. However, the work factor (a measure, under a given set of assumptions, of the requirements necessary for a specific analysis or attack against a cryptographic algorithm) required to break the algorithm must be sufficiently great. Included in the set of assumptions is the type of information expected to be available for cryptanalysis. For example, this could be ciphertext only; plaintext (not chosen) and corresponding ciphertext; chosen plaintext and corresponding ciphertext; or chosen ciphertext and corresponding recovered plaintext.

A strong cryptographic algorithm must satisfy the following conditions: (1) The algorithm's mathematical complexity prevents, for all practical purposes, solution through analytical methods. (2) The cost or time necessary to unravel the message or key is too great when mathematically less complicated methods are used, because either too many computational steps are involved (for example, in trying one key after another) or because too much storage space is required (for example, in an analysis requiring data accumulations such as dictionaries and statistical tables).

To be strong, the algorithm must satisfy the above conditions even when the analyst has the following advantages: (1) Relatively large amounts of plaintext (specified by the analyst, if so desired) and corresponding ciphertext are available. (2) Relatively large amounts of ciphertext (specified by the analyst, if so desired) and corresponding recovered plaintext are available. (3) All details of the algorithm are available to the analyst; that is, cryptographic strength cannot depend on the algorithm remaining secret. (4) Large high-speed computers are available for cryptanalysis.

Digital signatures

Digital signatures authenticate messages by ensuring that: the sender cannot later disavow messages; the receiver cannot forge messages or signatures; and the receiver can prove to others that the contents of a message are genuine and that the message originated with that particular sender. The digital signature is a function of the message, a secret key or keys possessed by the sender of the message, and sometimes data that are nonsecret or that may become nonsecret as part of the procedure (such as a secret key that is later made public).

Digital signatures are more easily obtained with public-key than with conventional algorithms. When a message is enciphered with a private key (known only to the originator), anyone deciphering the message with the public key can identify the originator. The latter cannot later deny having sent the message. Receivers cannot forge messages and signatures, since they do not possess the originator's private key.

Since enciphering and deciphering keys are identical in a conventional algorithm, digital signatures must be obtained in some other manner. One method is to use a set of keys to produce the signature. Some of the keys are made known to the receiver to permit signature verification, and the rest of the keys are retained by the originator in order to prevent forgery.

Data Encryption Standard

Regardless of the application, a cryptographic system must be based on a cryptographic algorithm of validated strength if it is to be acceptable. The Data Encryption Standard (DES) is such a validated conventional algorithm already in the public domain. This procedure enciphers a 64-bit block of plaintext into a 64-bit block of ciphertext under the control of a 56-bit key. The National Bureau of Standards accepted this algorithm as a standard, and it became effective on July 15, 1977.

Block ciphers

A block cipher (Fig. 1) transforms a string of input bits of fixed length (termed an input block) into a string of output bits of fixed length (termed an output block). In a strong block cipher, the enciphering and deciphering functions are such that every bit in the output block jointly depends on every bit in the input block and on every bit in the key. This property is termed intersymbol dependence.

Stream ciphers

A stream cipher (Fig. 2) employs a bit-stream generator to produce a stream of binary digits (0's and 1's) called a cryptographic bit stream, which is then combined either with plaintext (via the operator) to produce ciphertext or with ciphertext (via the ^-1 operator) to recover plaintext.

secret writing, a special system of changing ordinary writing for the purpose of making it intelligible only to a limited number of persons who know the system. Different methods of cryptography have been used for encoding military, diplomatic, business, illegal-political, and religious-heretical texts; they are also used in children’s guessing games, rebuses, and the like.

Cryptography has been known since very ancient times in the Orient, Greece, and Rome and in Russian texts from the 12th and 13th centuries. Besides its basic functions, cryptography was used in Old Slavonic manuscripts for distinguishing a religious text from commentaries, instructions to the reader, and so on, and as a magical device in exorcisms.

The basic known methods of cryptography are (1) use of another alphabet (such as the Glagolitic, Greek, or Latin alphabet in Russian texts); (2) changing the letters by adding marks or dropping parts of letters (what was called half-writing); (3) use of substitute symbols or numbers; (4) use of a different alphabetical order (what was called litoreia, for example) or of numbers corresponding to letters; (5) writing a text in the form of a certain design, sometimes concealed in another text (as an acrostic); (6) writing words in reverse order.

An inscription or document written cryptographically is called a cryptogram.