Cryptology ePrint Archive: Report 2015/589

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

A.-M. Leventi-Peetz and J.-V. Peetz

Abstract: 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. Motivation to this work were the results of recent articles 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.

Category / Keywords: secret-key cryptography / Algebraic cryptanalysis, algebraic attack resistance, multivariate quadratic polynomial equation system, S-box, SageMath, polynomial quotient ring, SAT solver, Rijndael AES, Lagrange polynomial, algebraic expression

Date: received 14 Jun 2015, last revised 16 Jun 2015

Contact author: leventi at t-online de

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Version: 20150621:162448 (All versions of this report)

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