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A new efficient algorithm for computing Gröbner bases (F4)
- J. Faugère
- Computer Science
- 1 June 1999
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
- J. Faugère
- Computer Science, MathematicsISSAC '02
- 10 July 2002
A new efficient algorithm for computing Gröbner bases is introduced that replaces the Buchberger criteria by an optimal criteria and it is proved that the resulting algorithm (called F5) generates no useless critical pairs if the input is a regular sequence.
Efficient Computation of Zero-Dimensional Gröbner Bases by Change of Ordering
The lexicographical GroBner basis can be obtained by applying this algorithm after a total degree Grobner basis computation: it is usually much faster to compute the basis this way than with a direct application of Buchberger's algorithm.
Algebraic Cryptanalysis of Hidden Field Equation (HFE) Cryptosystems Using Gröbner Bases
A new and efficient attack of this cryptosystem based on fast algorithms for computing Grobner basis is presented and it was possible to break the first HFE challenge in only two days of CPU time by using the new algorithm F5 implemented in C.
On the complexity of the BKW algorithm on LWE
- Martin R. Albrecht, Carlos Cid, J. Faugère, Robert Fitzpatrick, Ludovic Perret
- Computer Science, MathematicsDes. Codes Cryptogr.
- 11 July 2012
This work presents a study of the complexity of the Blum–Kalai–Wasserman (BKW) algorithm when applied to the Learning with Errors (LWE) problem, by providing refined estimates for the data and…
GeMSS: A Great Multivariate Short Signature
- Antoine Casanova, J. Faugère, Gilles Macario-Rat, Jacques Patarin, Ludovic Perret, Jocelyn Ryckeghem
- Computer Science, Mathematics
- 11 December 2017
The purpose of this document is to present GeMSS : a Great Multivariate Signature Scheme, a multivariate-based signature scheme producing small signatures and a fast verification process, and a medium/large public-key.
Algebraic Cryptanalysis of McEliece Variants with Compact Keys
It is proved that the private key of the McEliece cryptosystem satisfies a system of bi-homogeneous polynomial equations, which is due to the particular class of codes considered which are alternant codes.
Hybrid approach for solving multivariate systems over finite fields
This work presents a new general algorithm to solve multivariate polynomial systems over finite fields and gives theoretical evidences that this method brings a significant improvement in a very large context and clearly defines its limitations.
FGb: A Library for Computing Gröbner Bases
- J. Faugère
- Computer ScienceICMS
- 13 September 2010
FGb provides high quality implementations of state-of-the-art algorithms (F4 and F5) for computing Grobner bases, currently one of the best implementation of these algorithms, in terms of both speed and robustness.
On the complexity of Gröbner basis computation of semi-regular overdetermined algebraic equations
We extend the notion of regular sequence ([Mac16]) to overdetermined system of algebraic equations. We study generic properties of Grobner bases and analyse precisely the behavior of the F5 [Fau02]…