Work

Algorithm 1052: Evaluating a Boolean Polynomial on All Possible Inputs

Year: 2024

Type: article

Abstract: Evaluating a Boolean polynomial on all possible inputs (i.e., building the truth table of the corresponding Boolean function) is a simple computational problem that sometimes appears inside broader applications, for instance in cryptanalysis or in the implementation of more sophisticated algorithms to solve Boolean polynomial systems. Two techniques share the crown to perform this task: the Fast Exhaustive Search (FES) algorithm from 2010 (which is based on Gray Codes) and the space-efficient Moebius transform from 2021 (which is reminiscent of the FFT). Both require \(\mathcal{O}(d2^{n})\) operations for a degree- \(d\) Boolean polynomial on \(n\) variables and operate mostly in-place, but have other slightly different characteristics. They both provide an efficient iterator over the full truth table. This article describes BoolEAN POLynomial Evaluation (BeanPolE), a concise and flexible C library that implements both algorithms, as well as many other functions to deal with Boolean multivariate polynomials in dense representation.

Source: ACM Transactions on Mathematical Software

DOI: 10.1145/3699957

Author: Charles Bouillaguet

Institution: Sorbonne Université

Language: English

Topic: Polynomial and algebraic computation

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Agence Nationale de la Recherche, Centre National de la Recherche Scientifique

Awards: G1854824218, Algebraic cryptanalysis for post-quantum cryptography, Cryptanalyse de primitives cryptographiques classiques, Algorithmic Cryptanalysis wIth Actual Implementations