Self -corrective codes and their use in cryptography. Tarannikov Yu.V.

The book was written on the basis of special lecture courses “Theory of Coding and its application in cryptography” and “Theory of coding and its application to cryptography (additional chapters)” read by the author for more than ten years at the Mechanical and Mathematics faculty of Moscow State University since 2008 since 2008.

The book gives the necessary general information from the theory of self -corrective codes, while paying special attention to the applications in cryptography and related areas. The large chapter is devoted to Adamara matrices, Rida-Maller codes are discussed in detail, which are built with the help of maced functions and have a connection with non-linearity of maced functions-an important property required by the Boolean functions when they use cryptosystems as a knot. The necessary apparatus of work with Walsha coefficients is given.

in the methodically clear form, the Berleklekempa-Messi algorithm, which is an algorithm of double-purpose, is outlined: it effectively solves the problem of decoding the codes of the BPH and equally effectively allows you to restore the shift register with linear feedback of the smallest length, which generates at its disposal a piece of sequence. Such registers are used in the generation of pseudo -liable sequences and are an important part of many cryptosystems.

, based on self-correcting codes of the cryptosystem with an open key, including the cryptosystems of McElis and the Netherraiter, are discussed. The large chapter is devoted to orthogonal massifs - an object that has multiple use in mathematics and its applications. Binom orthogonal massifs without repeating lines are equivalent to the correlation-impressive maced functions, opposing correlation and other types of cryptographic attacks, as well as used in authentication codes. The last chapter of the theoretical part tells about the disjunctic codes used in the system separation systems. The book completes a large set of tasks that have undergone testing during the educational process.

For students, graduate students, teachers, all who are interested in the problems in question.