Boolean Ring Cryptographic Equation Solving

Sean Murphy; Maura Paterson; Christine Swart

Paper 2020/1255 Original: eprint.iacr.org/2020/1255 ↗

Boolean Ring Cryptographic Equation Solving

Sean Murphy

Maura Paterson

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: Preprint.
History: 2020-11-25: last updated; 2020-10-14: published
Short URL: https://ia.cr/2020/1255
License: https://creativecommons.org/licenses/by/4.0/

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},
      url = {https://eprint.iacr.org/2020/1255}
}