Un retour d'expérience sur le développement d'un code de recherche dans l'environnement PETSc

• Marc Medale (Polytech' Marseille)

Room: S112 PETSc is a suite of data structures and routines for the scalable (parallel) solution of scientific applications modeled by partial differential equations. It supports MPI, shared memory pthreads, and NVIDIA GPUs, as well as hybrid MPI-shared memory pthreads or MPI-GPU parallelism.

Linear Algebra for the Discrete Logarithm Problem using GPUs

• Jeljeli HAMZA (Loria, Nancy)

Room: S112 In the context of cryptanalysis, computing discrete logarithms in large cyclic groups using index-calculus-based methods, such as the number field sieve (NFS-DL) or the function field sieve (FFS), requires solving large sparse systems of linear equations modulo the group order. Most of the fast algorithms used to solve such systems -- e.g., the conjugate gradient or the Lanczos and Wiedemann algorithms -- iterate a product of the corresponding sparse matrix with a vector (SpMV). We investigate accelerating this central operation on NVIDIA GPUs. In this talk, we present a matrix format suitable to the sparsity and the specific computing model and how we use Residue Number System (RNS) arithmetic to accelerate modular operations.