Algebraic Analysis of a Simplified Encryption Algorithm GOST R 34.12-2015

• Main Authors: Evgenia Ishchukova, Ekaterina Maro, Pavel Pristalov
• Format: Article
• Language: English
• Published: MDPI AG 2020-05-01
• Series: Computation
• Subjects: S-box; systems of multivariate quadratic equations; algebraic analysis; SAT solving method; extended linearization method; GOST R 34.12-2015 encryption algorithms
• Online Access: https://www.mdpi.com/2079-3197/8/2/51

In January 2016, a new standard for symmetric block encryption was established in the Russian Federation. The standard contains two encryption algorithms: Magma and Kuznyechik. In this paper we propose to consider the possibility of applying the algebraic analysis method to these ciphers. To do this, we use the simplified algorithms Magma Å and S-KN2. To solve sets of nonlinear Boolean equations, we choose two different approaches: a reduction and solving of the Boolean satisfiability problem (by using the CryptoMiniSat solver) and an extended linearization method (XL). In our research, we suggest using a security assessment approach that identifies the resistance of block ciphers to algebraic cryptanalysis. The algebraic analysis of an eight-round Magma (68 key bits were fixed) with the CryptoMiniSat solver demanded four known text pairs and took 3029.56 s to complete (the search took 416.31 s). The algebraic analysis of a five-round Magma cipher with weakened S-boxes required seven known text pairs and took 1135.61 s (the search took 3.36 s). The algebraic analysis of a five-round Magma cipher with disabled S-blocks (equivalent value substitution) led to getting only one solution for five known text pairs in 501.18 s (the search took 4.92 s). The complexity of the XL algebraic analysis of a four-round S-KN2 cipher with three text pairs was 236.33 s (took 1.191 Gb RAM).