Boolean Ring Cryptographic Equation Solving

Sean Murphy; Maura Paterson; Christine Swart

Paper 2020/1255

Boolean Ring Cryptographic Equation Solving

Sean Murphy, Maura Paterson, and Christine Swart

Abstract

This paper considers multivariate polynomial equation systems over GF(2) that have a small number of solutions. This paper gives a new method EGHAM2 for solving such systems of equations that uses the properties of the Boolean quotient ring to potentially reduce memory and time complexity relative to existing XL-type or Groebner basis algorithms applied in this setting. This paper also establishes a direct connection between solving such a multivariate polynomial equation system over GF(2), an MQ problem, and an instance of the LPN problem.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. to appear in SAC2020
Keywords: MQ problem XL algorithm Groebner basis Boolean ring LPN problem.
Contact author(s): s murphy @ rhul ac uk
History: 2020-11-25: revised; 2020-10-14: received; See all versions
Short URL: https://ia.cr/2020/1255
License: CC BY

BibTeX

@misc{cryptoeprint:2020/1255,
      author = {Sean Murphy and Maura Paterson and Christine Swart},
      title = {Boolean Ring Cryptographic Equation Solving},
      howpublished = {Cryptology ePrint Archive, Paper 2020/1255},
      year = {2020},
      note = {\url{https://eprint.iacr.org/2020/1255}},
      url = {https://eprint.iacr.org/2020/1255}
}