Public Key

Abstract

Recall that a cryptosystem consists of a 1-to-1 enciphering transformation f from a set P of all possible plaintext message units to a set C of all possible ciphertext message units. Actually, the term “cryptosystem” is more often used to refer to a whole family of such transformations, each corresponding to a choice of parameters (the sets P and C, as well as the map f, may depend upon the values of the parameters). For example, for a fixed N-letter alphabet (with numerical equivalents also fixed once and for all), we might consider the affine cryptosystem (or “family of cryptosystems”) which for each a ∊ (Z/NZ)* and b ∊ Z/NZ is the map from P = Z/NZ to C = Z/NZ defined by C = aP + b mod N. In this example, the sets P and C are fixed (because N is fixed), but the enciphering transformation f depends upon the choice of parameters a, b. The enciphering transformation can then be described by (i) an algorithm, which is the same for the whole family, and (ii) the values of the parameters. The values of the parameters are called the enciphering key K _E . In our example, K _E is the pair (a, b). In practice, we shall suppose that the algorithm is publicly known, i.e., the general procedure used to encipher cannot be kept secret. However, the keys can easily be changed periodically and, if one wants, kept secret.