Murphy, Sean

Paterson, Maura

Swart, Christine

English

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

Royal Holloway - Pure

Boolean Ring Cryptographic Equation Solving

https://pure.royalholloway.ac.uk/portal/files/39458567/BooleRing_Crypto_07Oct20.pdf

Boolean Ring Cryptographic Equation Solving

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Royal Holloway - Pure