Криптография

A special case of multi-alphabet substitution is the Vigenere cipher. The encryption key is a set of m integers: k = (k1, k2, ..., km). The procedure for converting the plaintext t = (t1, t2, ...) into a ciphertext c = (c1, c2, ...) is based on generalized Caesar cipher: c1 = t1 + k1 (mod 26), c2 = t2 + k2 (mod 26) , etc. In fact, the encryption key is an infinite sequence formed by the periodic repetition of the initial set: k1, k2, ..., km, k1, k2, ..., km, k1, k2, ... This sequence is called cryptographic bit stream.Transposition ciphersIn another class of ciphers called transposition the letters of the message are adjusted to each other in some way. Scytale cipher belongs to this class.Path transposition and column transposition refer to class of transposition. The message is entered in the box [n × m] according to pre-deterministic method and the columns are numbered either in usual sequence, or key letter sequence.Symmetric cryptosystemsBasics of symmetric cryptosystemsAll asymmetric cryptographic systems are based on application of one-way functions with a secret. The function F: X → Y is called a one-way function, if the following conditions are met [7]:1) there is an efficient algorithm that computes F(x) for any x∈X;2) there is no efficient algorithm for inverting the function F.One-way function with a secret is a function Fk: X → Y that depends on parameter k∈K (this option is called a secret), which satisfies the following conditions:1) for any k∈K there is an efficient algorithm that computes Fk(x) for any x∈X;2) with indeterminate k there is no efficient algorithm to invert the function Fk;3) with determinate k there is an efficient algorithm to invert the function Fk.Each requester selects a cryptographic one-way function Ek with a secret k. Functions are entered in a public directory, but the secret value k is kept a secret. If the requester B wants to send a message t to the requester A, it extracts function Ek of requester A from the directory and computes c = Ek(t). Ciphertext c is sent to the requester A, who calculates the original message twith c, inverting function Ek with the secret k [8]. RSA cryptosystemsWhen using the RSA system, each user creates a secret and public key as follows:Select two large unequal primes p and q, calculate n=pq and m=(p-1)(q-1).2) Select an integer e with e