**Boolean Ring Cryptographic Equation Solving.** / Murphy, Sean; Paterson, Maura; Swart, Christine.

Research output: Working paper

Forthcoming

**Boolean Ring Cryptographic Equation Solving.** / Murphy, Sean; Paterson, Maura; Swart, Christine.

Research output: Working paper

Murphy, S, Paterson, M & Swart, C 2020 'Boolean Ring Cryptographic Equation Solving'.

Murphy, S., Paterson, M., & Swart, C. (Accepted/In press). *Boolean Ring Cryptographic Equation Solving*.

Murphy S, Paterson M, Swart C. Boolean Ring Cryptographic Equation Solving. 2020 Sep 18.

@techreport{cdf3999441aa4e9a85181be1a5b7fdf0,

title = "Boolean Ring Cryptographic Equation Solving",

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.",

author = "Sean Murphy and Maura Paterson and Christine Swart",

year = "2020",

month = sep,

day = "18",

language = "English",

type = "WorkingPaper",

}

TY - UNPB

T1 - Boolean Ring Cryptographic Equation Solving

AU - Murphy, Sean

AU - Paterson, Maura

AU - Swart, Christine

PY - 2020/9/18

Y1 - 2020/9/18

N2 - 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.

AB - 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.

UR - https://eprint.iacr.org/2020/1255

M3 - Working paper

BT - Boolean Ring Cryptographic Equation Solving

ER -