Computer algebra in coding theory and cryptanalysis

Stanislav Bulygin, 2009
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The book "Computer Algebra in Coding Theory and Cryptanalysis" by Stanislav Bulygin, based on the author's dissertation, focuses on the application of symbolic methods to solve problems in the field of decoding linear codes and algebraic cryptanalysis. It reformulates the original problems in the form of systems of polynomial equations over a finite field, whose solutions provide pathways to solving the initial problems. The use of Gröbner bases for solving these systems is discussed in detail. The first part of the book concentrates on the decoding of linear codes, introducing a novel method applicable to arbitrary linear codes. The second part addresses the algebraic cryptanalysis of AES, developing an approach that eliminates redundant auxiliary variables and solves a system solely in terms of the key variables. These approaches prove particularly effective for small variants of AES, especially when using multiple plaintext/ciphertext pairs.

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