Generating S-Box Multivariate Quadratic Equation Systems And Estimating Algebraic Attack Resistance Aided By SageMath

Methods are presented to derive with the aid of the computer mathematics software system SageMath the Multivariate Quadratic equation systems (MQ) for the input and output bit variables of a cryptographic S-box starting from its algebraic expressions. Motiva-tion to this work were the results of recent articles [4, 5, 6] which we have verified and extended in an original way, to our knowledge, not yet published elsewhere. At the same time we present results contrary to the published ones which cast serious doubts on the suitability of previously presented formulas, supposed to quantify the resistance of S-boxes against algebraic attacks. Key Words – Algebraic cryptanalysis, algebraic attack resistance, multivariate quadratic polynomial equation system, S-box, SageMath, polynomial quotient ring, SAT solver, Rijndael AES, Lagrange poly-nomial, algebraic expression