[PDF][PDF] GeMSS: a great multivariate short signature
A Casanova, JC Faugere, G Macario-Rat, J Patarin… - 2017 - inria.hal.science
1 Introduction sparkling GeMSS spring up from the night sky a dazzling splendor to ever
beautify sequined glories that verily eye smack sparkling GeMSS spring up from night sky …
beautify sequined glories that verily eye smack sparkling GeMSS spring up from night sky …
Practical post-quantum signature schemes from isomorphism problems of trilinear forms
In this paper, we propose a practical signature scheme based on the alternating trilinear
form equivalence problem. Our scheme is inspired by the Goldreich-Micali-Wigderson's zero …
form equivalence problem. Our scheme is inspired by the Goldreich-Micali-Wigderson's zero …
On the complexity of the rank syndrome decoding problem
In this paper, we propose two new generic attacks on the rank syndrome decoding (RSD)
problem. Let C be a random [n, k] rank code over GF (qm) and let y= x+ e be a received …
problem. Let C be a random [n, k] rank code over GF (qm) and let y= x+ e be a received …
Design principles for HFEv-based multivariate signature schemes
Abstract The Hidden Field Equations (HFE) Cryptosystem as proposed by Patarin is one of
the best known and most studied multivariate schemes. While the security of the basic …
the best known and most studied multivariate schemes. While the security of the basic …
Improvement of algebraic attacks for solving superdetermined MinRank instances
M Bardet, M Bertin - International Conference on Post-Quantum …, 2022 - Springer
The MinRank (MR) problem is a computational problem that arises in many cryptographic
applications. In Verbel et al., the authors introduced a new way to solve superdetermined …
applications. In Verbel et al., the authors introduced a new way to solve superdetermined …
Exact algorithms for linear matrix inequalities
Let A(x)=A_0+x_1A_1+⋯+x_nA_n be a linear matrix, or pencil, generated by given
symmetric matrices A_0,A_1,...,A_n of size m with rational entries. The set of real vectors x …
symmetric matrices A_0,A_1,...,A_n of size m with rational entries. The set of real vectors x …
Solving multivariate polynomial systems and an invariant from commutative algebra
A Caminata, E Gorla - Arithmetic of Finite Fields: 8th International …, 2021 - Springer
The complexity of computing the solutions of a system of multivariate polynomial equations
by means of Gröbner bases computations is upper bounded by a function of the solving …
by means of Gröbner bases computations is upper bounded by a function of the solving …
Mira: a digital signature scheme based on the minrank problem and the mpc-in-the-head paradigm
We exploit the idea of [Fen22] which proposes to build an efficient signature scheme based
on a zero-knowledge proof of knowledge of a solution of a MinRank instance. The scheme …
on a zero-knowledge proof of knowledge of a solution of a MinRank instance. The scheme …
Solving parametric systems of polynomial equations over the reals through Hermite matrices
HP Le, MS El Din - Journal of Symbolic Computation, 2022 - Elsevier
We design a new algorithm for solving parametric systems of equations having finitely many
complex solutions for generic values of the parameters. More precisely, let f=(f 1,…, fm)⊂ Q …
complex solutions for generic values of the parameters. More precisely, let f=(f 1,…, fm)⊂ Q …
Refined f5 algorithms for ideals of minors of square matrices
S Gopalakrishnan, V Neiger… - Proceedings of the 2023 …, 2023 - dl.acm.org
We consider the problem of computing a grevlex Gröbner basis for the set Fr (M) of minors of
size r of an n× n matrix M of generic linear forms over a field of characteristic zero or large …
size r of an n× n matrix M of generic linear forms over a field of characteristic zero or large …