A special case of multi-alphabet substitution is the Vigenere cipher. T he encryption key is a set of m integers: k = (k1, k2, …, km). T he 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.
I n 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. S cytale cipher belongs to this class. Path transposition and column transposition refer to class of transposition. T he message is entered in the box [n x 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.
T he 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. F unctions are entered in a public directory, but the secret value k is kept a secret. I f 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). C iphertext 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 <m and GCD (e, m) = 1 3) Calculate the number of d satisfying the condition: ed = 1 (mod m).4) The secret key is (p, q, d), the public key is (n, e).5) The public keys of all requesters are placed in public directory. The encryption function represented in terms of the number t (t <n) in RSA system is determined by the formula: E (t) = te (mod n). T he decryption function (which depends on the secret key) is given by: D© = cd (mod n).
T he long message is divided into blocks of log2n length (each block is a number less than n), each block is encrypted and then decrypted separately. Features of asymmetric cryptosystems applicationAccording to the effectiveness and strength the asymmetrical systemsare low compared to symmetric systems. T herefore, asymmetrical systems areusually used for encryption in combination with symmetric systems.
F or example, encryption using a symmetric algorithm A1and asymmetric algorithm A2 is performed as follows:1) a random key k1 for A1 algorithm is generated;2) data encryption is performed with this key: c'= A1(t, k1);3) k1 key is encrypted with the algorithm A2on the public key kp: c''=A2(k1, kp).4) ciphertext is a pair of c = (c', c'').In order to decode the received message (c', c''), the recipient restores the key k1 with c'', with which decrypts the original text with c'. Since the length of the key k1 is small compared to the length of the text, such a scheme gives a considerable gain in speed. ConclusionSumming up the results of our study, it should be noted that it is difficult to reliably protect your secrets. S pecialist in any situation expresses doubts about the reliability of protection offered. I t is recommended not to show off the algorithm. E.
ven if you were able to prove the theorem that the attacks of your protection system are algorithmically unsolvable, do not relax. T ry to understand why the conditions are not met in the case. A nd finally follow the principle of privacy protection. H.
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