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 …

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 …

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 …

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 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 …

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 …

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 …

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 …

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 …

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 …