Solving the problem of Boolean satisfiability for estimating the security of block ciphers Magma and PRESENT to algebraic cryptanalysis

Some results of experimental investigating algorithms for cryptanalysis of ciphers Magma and PRESENT are presented. Algorithms under investigation solve the systems of Boolean equations of these ciphers by known methods – SAT and XL. The ciphers under consideration have been taken with small numbers of rounds (3, 4 in PRESENT, 5,8 in Magma) and simplified S-boxes (identical, linearized in Magma). The experimental results (memory size, running time, number of addition operations) are presented in dependence on the numbers of plain/cipher texts, equations, unknowns, etc. For example, the $8$-round cipher Magma with 5376 equations, 2048 unknowns is analysed by a computer with the processor IntelCore i5 for 416.31 sec.