A variant of the F4 algorithm

Antoine Joux; Vanessa Vitse

Paper 2010/158

A variant of the F4 algorithm

Antoine Joux and Vanessa Vitse

Abstract

Algebraic cryptanalysis usually requires to find solutions of several similar polynomial systems. A standard tool to solve this problem consists of computing the Gröbner bases of the corresponding ideals, and Faugère's F4 and F5 are two well-known algorithms for this task. In this paper, we present a new variant of the F4 algorithm which is well suited to algebraic attacks of cryptosystems since it is designed to compute Gröbner bases of a set of polynomial systems having the same shape. It is faster than F4 as it avoids all reductions to zero, but preserves its simplicity and its computation efficiency, thus competing with F5.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Unknown where it was published
Keywords: Gröbner basis F4 F5 multivariate cryptography algebraic cryptanalysis
Contact author(s): vanessa vitse @ prism uvsq fr
History: 2010-03-24: received
Short URL: https://ia.cr/2010/158
License: CC BY

BibTeX

@misc{cryptoeprint:2010/158,
      author = {Antoine Joux and Vanessa Vitse},
      title = {A variant of the F4 algorithm},
      howpublished = {Cryptology {ePrint} Archive, Paper 2010/158},
      year = {2010},
      url = {https://eprint.iacr.org/2010/158}
}