MRHS Solver Based on Linear Algebra and Exhaustive Search

Håvard Raddum; Pavol Zajac

Paper 2018/111

MRHS Solver Based on Linear Algebra and Exhaustive Search

Håvard Raddum and Pavol Zajac

Abstract

We show how to build a binary matrix from the MRHS representation of a symmetric-key cipher. The matrix contains the cipher represented as an equation system and can be used to assess a cipher's resistance against algebraic attacks. We give an algorithm for solving the system and compute its complexity. The complexity is normally close to exhaustive search on the variables representing the user-selected key. Finally, we show that for some variants of LowMC, the joined MRHS matrix representation can be used to speed up regular encryption in addition to exhaustive key search.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Preprint.
Keywords: Algebraic cryptanalysis MRHS LowMC
Contact author(s): pavol zajac @ stuba sk
History: 2018-01-30: received
Short URL: https://ia.cr/2018/111
License: CC BY

BibTeX

@misc{cryptoeprint:2018/111,
      author = {Håvard Raddum and Pavol Zajac},
      title = {{MRHS} Solver Based on Linear Algebra and Exhaustive Search},
      howpublished = {Cryptology {ePrint} Archive, Paper 2018/111},
      year = {2018},
      url = {https://eprint.iacr.org/2018/111}
}