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Conference Papers Year : 2022

A Simple Deterministic Algorithm for Systems of Quadratic Polynomials over F 2

Abstract

This article discusses a simple deterministic algorithm for solving quadratic Boolean systems which is essentially a special case of more sophisticated methods. The main idea fits in a single sentence: guess enough variables so that the remaining quadratic equations can be solved by linearization (i.e. by considering each remaining monomial as an independent variable and solving the resulting linear system). Under strong heuristic assumptions, this finds all the solutions of m quadratic polynomials in n variables with Õ(2^(n− √ 2m)) operations. Although the best known algorithms require exponentially less time, the present technique has the advantage of being simpler to describe and easy to implement. In strong contrast with the state-of-the-art, it is also quite efficient in practice. 2012
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Dates and versions

hal-03363031 , version 1 (02-10-2021)

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Charles Bouillaguet, Claire Delaplace, Monika Trimoska. A Simple Deterministic Algorithm for Systems of Quadratic Polynomials over F 2. Symposium on Simplicity in Algorithms (SOSA), SIAM, Jan 2022, Alexandria, United States. pp.285-296, ⟨10.1137/1.9781611977066.22⟩. ⟨hal-03363031⟩
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