A multivariate cryptograpic instance in practice is a multivariate polynomial system. So the
security of a protocol rely on the complexity of solving a multivariate polynomial system. In …

Gröbner basis methods are used to solve systems of polynomial equations over finite fields,
but their complexity is poorly understood. In this work an upper bound on the time complexity …

The security of multivariate cryptosystems and digital signature schemes relies on the
hardness of solving a system of polynomial equations over a finite field. Polynomial system …

This chapter considers the known techniques to solve (systems of) nonlinear polynomial
equations. After giving a historical overview of the topic, we describe algorithms to solve …

Abstract The Joux--Vitse Crossbred algorithm's aim is to efficiently solve a system of semi-
regular multivariate polynomials equations. The authors tested their algorithm for boolean …

In this thesis we study two major topics in cryptanalysis and optimization: software algebraic
cryptanalysis and elliptic curve optimizations in cryptanalysis. The idea of algebraic …

Semi-regular sequences over F 2 are sequences of homogeneous elements of the algebra
B (n)= F 2 [X 1,..., X n]/(X 1 2,..., X n 2), which have as few relations between them as …

Introducción y motivación:“La criptografía de curva elíptica no es la solución a largo plazo
que esperábamos que fuera. Por tanto, nos hemos visto obligados a replantear nuestra …

Semi-regular sequences over F 2 are sequences of homogeneous elements of the algebra
B (n)= F 2 [X 1,..., X n]/(X 1 2,..., X n 2), which have a given Hilbert series and can be thought …

This thesis analyses the assumptions present in security proofs of post-quantum
cryptosystems using Koblitz and Menezes' critique to guide the focus points. The classical …