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Криптография

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Contents
Introduction 3
1. The history of cryptography 4
2. Basic concepts of cryptography 6
2.1. Subject of cryptography 6
2.2. Cryptographic system model 7
2.3. Formal model and code classification 8
3. Symmetric cryptosystems 9
3.1. Substitution ciphers 9
3.2. Transposition ciphers 10
4. Symmetric cryptosystems 10
4.1. Basics of symmetric cryptosystems 10
4.2. RSA cryptosystems 11
5. Features of asymmetric cryptosystems application 12
Conclusion 12
References 13

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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 <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). The decryption function (which depends on the secret key) is given by: D(c) = cd (mod n). The 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. Therefore, asymmetrical systems areusually used for encryption in combination with symmetric systems. For 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. Specialist in any situation expresses doubts about the reliability of protection offered. It is recommended not to show off the algorithm. Even if you were able to prove the theorem that the attacks of your protection system are algorithmically unsolvable, do not relax. Try to understand why the conditions are not met in the case. And finally follow the principle of privacy protection. Having the best security system created, make sure it is protected.ReferencesBauer, F.L. (2007). Decrypted Secrets - Methods and Maxims of Cryptology, Springer.Schneier, В. (1996). Applied Cryptography: Protocols, Algorithms, and Source Code in C, New York : Wiley.Singh, S. (1999).The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography, New York. Wenbo Mao. (2003). Modern Cryptography: Theory and Practice. Hewlett-Packard Company, Prentice Hall PTR.Алферов А.П.,Зубов А.Ю.,Кузьмин А.С.,Черемушкин А.В. Основы криптографии: Учебное пособие. — М.: Гелиос АРВ, 2001. — 480 с. Баричев С.Г., Гончаров В.В., Меров Р.Е. Основы современной криптографии. - М., 2001.Введение в криптографию. / Под ред. В.В. Ященко. — 2-е изд., испр. — М.: МЦНМО: «ЧеРо», 1999. — 272 с.Дориченко С.А., Ященко В.В. 25 этюдов о шифрах. — М.: «ТЕИС», 1994. — 69 с.Жельников В. Криптография от папируса до компьютера. - М., 1996.

Список литературы [ всего 9]


References
1. Bauer, F.L. (2007). Decrypted Secrets - Methods and Maxims of Cryptology, Springer.
2. Schneier, В. (1996). Applied Cryptography: Protocols, Algorithms, and Source Code in C, New York : Wiley.
3. Singh, S. (1999).The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography, New York.
4. Wenbo Mao. (2003). Modern Cryptography: Theory and Practice. Hewlett-Packard Company, Prentice Hall PTR.
5. Алферов А.П., Зубов А.Ю., Кузьмин А.С., Черемушкин А.В. Основы криптографии: Учебное пособие. — М.: Гелиос АРВ, 2001. — 480 с.
6. Баричев С.Г., Гончаров В.В., Меров Р.Е. Основы современной криптографии. - М., 2001.
7. Введение в криптографию. / Под ред. В.В. Ященко. — 2-е изд., испр. — М.: МЦНМО: «ЧеРо», 1999. — 272 с.
8. Дориченко С.А., Ященко В.В. 25 этюдов о шифрах. — М.: «ТЕИС», 1994. — 69 с.
9. Жельников В. Криптография от папируса до компьютера. - М., 1996.
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