Search Results - "Jean-Charles Faugere"

A survey on signature-based algorithms for computing Gröbner bases by Eder, Christian, Faugère, Jean-Charles

“…In 1965 Buchberger introduced an algorithmic approach to compute Gröbner bases. Later on, he and many others presented various attempts to improve the…”
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Sparse FGLM algorithms by Faugère, Jean-Charles, Mou, Chenqi

“…Given a zero-dimensional ideal I⊂K[x1,…,xn] of degree D, the transformation of the ordering of its Gröbner basis from DRL to LEX is a key step in polynomial…”
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Cryptanalysis of HFE, multi-HFE and variants for odd and even characteristic by Bettale, Luk, Faugère, Jean-Charles, Perret, Ludovic

“…We investigate in this paper the security of HFE and Multi-HFE schemes as well as their minus and embedding variants. Multi-HFE is a generalization of the…”
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Polynomial-division-based algorithms for computing linear recurrence relations by Berthomieu, Jérémy, Faugère, Jean-Charles

“…Sparse polynomial interpolation, sparse linear system solving or modular rational reconstruction are fundamental problems in Computer Algebra. They come down…”
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Cryptanalysis of the extension field cancellation cryptosystem by Chakraborty, Olive, Faugère, Jean-Charles, Perret, Ludovic

“…In this article, we present algebraic attacks against the Extension Field Cancellation ( EFC ) scheme, a multivariate public-key encryption scheme which was…”
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Computing critical points for invariant algebraic systems by Faugère, Jean-Charles, Labahn, George, Safey El Din, Mohab, Schost, Éric, Vu, Thi Xuan

“…Let K be a field and (f1,…,fs,ϕ) be multivariate polynomials in K[x1,…,xn] (with s<n) each invariant under the action of Sn, the group of permutations of…”
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A Distinguisher for High-Rate McEliece Cryptosystems by Faugere, Jean-Charles, Gauthier-Umana, Valerie, Otmani, Ayoub, Perret, Ludovic, Tillich, Jean-Pierre

“…The Goppa Code Distinguishing (GD) problem consists in distinguishing the matrix of a Goppa code from a random matrix. The hardness of this problem is an…”
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Linear algebra for computing Gröbner bases of linear recursive multidimensional sequences by Berthomieu, Jérémy, Boyer, Brice, Faugère, Jean-Charles

“…The so-called Berlekamp–Massey–Sakata algorithm computes a Gröbner basis of a 0-dimensional ideal of relations satisfied by an input table. It extends the…”
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A nearly optimal algorithm to decompose binary forms by Bender, Matías R., Faugère, Jean-Charles, Perret, Ludovic, Tsigaridas, Elias

“…Symmetric tensor decomposition is an important problem with applications in several areas, for example signal processing, statistics, data analysis and…”
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On the complexity of solving quadratic Boolean systems by Bardet, Magali, Faugère, Jean-Charles, Salvy, Bruno, Spaenlehauer, Pierre-Jean

“…A fundamental problem in computer science is that of finding all the common zeros of m quadratic polynomials in n unknowns over F2. The cryptanalysis of…”
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Hybrid approach for solving multivariate systems over finite fields by Bettale Luk, Faugère Jean-Charles, Perret Ludovic

“…In this paper, we present an improved approach to solve multivariate systems over finite fields. Our approach is a tradeoff between exhaustive search and…”
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Structural cryptanalysis of McEliece schemes with compact keys by Faugère, Jean-Charles, Otmani, Ayoub, Perret, Ludovic, de Portzamparc, Frédéric, Tillich, Jean-Pierre

“…A very popular trend in code-based cryptography is to decrease the public-key size by focusing on subclasses of alternant/Goppa codes which admit a very…”
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On the complexity of the generalized MinRank problem by Faugère, Jean-Charles, Safey El Din, Mohab, Spaenlehauer, Pierre-Jean

“…We study the complexity of solving the generalized MinRank problem, i.e. computing the set of points where the evaluation of a polynomial matrix has rank at…”
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Polynomial-time algorithms for quadratic isomorphism of polynomials: The regular case by Berthomieu, Jérémy, Faugère, Jean-Charles, Perret, Ludovic

“…Let f=(f1,…,fm) and g=(g1,…,gm) be two sets of m≥1 nonlinear polynomials in K[x1,…,xn] (K being a field). We consider the computational problem of finding–if…”
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On the complexity of computing Gröbner bases for weighted homogeneous systems by Faugère, Jean-Charles, Safey El Din, Mohab, Verron, Thibaut

“…Solving polynomial systems arising from applications is frequently made easier by the structure of the systems. Weighted homogeneity (or quasi-homogeneity) is…”
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Using Symmetries in the Index Calculus for Elliptic Curves Discrete Logarithm by Faugère, Jean-Charles, Gaudry, Pierrick, Huot, Louise, Renault, Guénaël

“…In 2004, an algorithm is introduced to solve the DLP for elliptic curves defined over a non-prime finite field . One of the main steps of this algorithm…”
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Algebraic Cryptanalysis of McEliece Variants with Compact Keys by Faugère, Jean-Charles, Otmani, Ayoub, Perret, Ludovic, Tillich, Jean-Pierre

“…In this paper we propose a new approach to investigate the security of the McEliece cryptosystem. We recall that this cryptosystem relies on the use of…”
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Gröbner bases of bihomogeneous ideals generated by polynomials of bidegree ( 1 , 1 ) : Algorithms and complexity by Faugère, Jean-Charles, Safey El Din, Mohab, Spaenlehauer, Pierre-Jean

“…Solving multihomogeneous systems, as a wide range of structured algebraic systems occurring frequently in practical problems, is of first importance…”
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Polly Cracker, revisited by Albrecht, Martin R., Faugère, Jean-Charles, Farshim, Pooya, Herold, Gottfried, Perret, Ludovic

“…We formally treat cryptographic constructions based on the hardness of deciding ideal membership in multivariate polynomial rings. Of particular interest to us…”
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On the relation between the MXL family of algorithms and Gröbner basis algorithms by Albrecht, Martin R., Cid, Carlos, Faugère, Jean-Charles, Perret, Ludovic

“…The computation of Gröbner bases remains one of the most powerful methods for tackling the Polynomial System Solving (PoSSo) problem. The most efficient known…”
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