MQ Soft : A fast multivariate cryptography library
MQsoft is an efficient library in C for post-quantum multivariate-based cryptography. It includes HFE-based schemes such GeMSS, Gui and DualModeMS. Our library is modular and permits to perform fundamental arithmetic operations over finite fields: efficient constant-time arithmetic in GF(2^n), finding the roots of a univariate polynomial in GF(2^n)[X], evaluate efficiently multivariate quadratic systems in GF(2) (in constant-time and in variable-time), etc ...
Project Leader : Ludovic Perret
01/2023
msolve : Multivariate polynomial systems solving
msolve is a C library for solving multivariate polynomial systems. It relies on algebraic algorithms, in particular Gröbner bases. It allows the user to solve exactly polynomial systems with rational coefficients (real root isolation) and coefficients in a finite field (of cardinality < 2^31).
msolve provides high-performance implementations of algorithms which are known to be beyond the most efficient in this area. The library can be used through various computer algebra systems and is already integrated in OSCAR and SageMath.
msolve is developed in collaboration with Christian Eder (TU Kaiserslautern, Germany).
Project Leader : Mohab Safey El Din
10/2022
PML : Polynomial Matrix Library
This library provides additions to NTL: efficient implementations for operations on univariate polynomial matrices and structured scalar matrices, and some uses of these for related algebraic computations. Work in progress includes adding functionalities (algebraic relations, normal form computation) and providing similar additions based on Flint.
Project Leader : Vincent Neiger
01/2023