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Communication Dans Un Congrès Année : 2018

A crossbred algorithm for solving Boolean polynomial systems

Vanessa Vitse
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Résumé

We consider the problem of solving multivariate systems of Boolean polynomial equations: starting from a system of m polynomials of degree at most d in n variables, we want to find its solutions over F2. Except for d = 1, the problem is known to be NP-hard, and its hardness has been used to create public cryptosystems; this motivates the search for faster algorithms to solve this problem. After reviewing the state of the art, we describe a new algorithm and show that it outperforms previously known methods in a wide range of relevant parameters. In particular, the first named author has been able to solve all the Fukuoka Type I MQ challenges, culminating with the resolution of a system of 148 quadratic equations in 74 variables in less than a day (and with a lot of luck).
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Dates et versions

hal-01981516 , version 1 (15-01-2019)

Identifiants

  • HAL Id : hal-01981516 , version 1

Citer

Antoine Joux, Vanessa Vitse. A crossbred algorithm for solving Boolean polynomial systems. NuTMiC 2017, 2017, Varsovie, Poland. pp.3-21. ⟨hal-01981516⟩
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