Boolean Ring Cryptographic Equation Solving

Sean Murphy, Maura Paterson, Christine Swart

Research output: Working paper

63 Downloads (Pure)


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.
Original languageEnglish
Number of pages21
Publication statusPublished - 18 Sept 2020

Publication series


Cite this