Biblio

In this paper, we examine algebraic attacks on the O'zDSt 1105:2009. We begin with a brief review of the meaning of algebraic cryptanalysis, followed by an algebraic cryptanalysis of O'zDSt 1105:2009. Primarily O'zDSt 1105:2009 encryption algorithm is decomposed and each transformation in it is algebraic described separately. Then input and output of each transformation are expressed with other transformation, encryption key, plaintext and cipher text. Created equations, unknowns on it and degree of unknowns are analyzed, and then overall result is given. Based on experimental results, it is impossible to save all system of equations that describes all transformations in O'zDSt 1105:2009 standard. Because, this task requires 273 bytes for the second round. For this reason, it is advisable to evaluate the parameters of the system of algebraic equations, representing the O'zDSt 1105:2009 standard, theoretically.

In this paper we present results of algebraic analysis of GOST⌖ algorithm in SageMath environment. Using the GOST⌖ as the example we explore basic stages of algebraic analysis of any symmetric block cipher based on Feistel network. We construct sets of boolean equations for five encryption rounds and determine the number of known text pairs for which the key can be found with the probability of 1. The algebraic analysis of five rounds of GOST⌖ allowed to find a 160-bit encryption key with the probability of 1 for five known text pairs within 797.21 s; the search for the solution took 24.66 s.