Algebraic Cryptanalysis of Block Ciphers

Abstract

Algebraic methods of cryptanalysis are applicable to present-day ciphers. These methods are based on generation of an equation system, where elements of a ciphertext and a key are chosen as variables of the system. When implementing a linearization method to solve the equation system, we consider a possibility to find partial elements of a key. Generally, cryptosystems use S-blocks, which are the only element contributing to nonlinearity of a ciphering transformation and the level of its strength against cryptanalytic attacks. In this paper we present, by the example of encryption algorithm Kuznechik, an algebraic analysis applicable to some block ciphers.

Evaluation of the strength and performance of a new hashing algorithm based on a block cipher

“…The first step needs to be performed only once for the cryptographic algorithm under consideration. The most commonly used methods for solving equations include linearization algorithms [23]- [25], Gröbner basis [26], and reduction to the SAT problem [27]. Linearization solves the resulting system of non-linear equations by replacing non-linear terms with new variables, so each non-linear monomial is replaced by a new variable.…”