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

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

Paper 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.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Preprint. MINOR revision.
Keywords: Algebraic cryptanalysis algebraic attack resistance S-box SageMath polynomial quotient ring SAT solver Rijndael AES Lagrange polynomial algebraic expression
Contact author(s): leventi @ t-online de
History: 2015-06-21: received
Short URL: https://ia.cr/2015/589
License: CC BY

BibTeX

@misc{cryptoeprint:2015/589,
      author = {A. -M.  Leventi-Peetz and J. -V.  Peetz},
      title = {Generating S-Box Multivariate Quadratic Equation Systems And Estimating   Algebraic Attack Resistance Aided By {SageMath}},
      howpublished = {Cryptology {ePrint} Archive, Paper 2015/589},
      year = {2015},
      url = {https://eprint.iacr.org/2015/589}
}