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 cryptanalysisalgebraic attack resistanceS-boxSageMathpolynomial quotient ringSAT solverRijndael AESLagrange polynomialalgebraic expression
Contact author(s)
leventi @ t-online de
History
2015-06-21: received
Short URL
https://ia.cr/2015/589
License
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2015/589}},
      url = {https://eprint.iacr.org/2015/589}
}
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