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 language | English |
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Publisher | Springer |
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Pages | 252-272 |
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Number of pages | 21 |
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Volume | 12804 |
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Publication status | Published - 18 Sept 2020 |
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