Improvement in the filtering step of integer factorization algorithms

Cyril Bouvier (1)

1 CARAMEL - Cryptology, Arithmetic: Hardware and Software

The security of the RSA public-key cryptosystem is based on the difficulty of factoring large integers which have exactly two prime factors of approximately the same size. Most factoring algorithms aiming at RSA moduli (Quadratic Sieve and Number Field Sieve), can be described in 3 main steps: data collection, filtering and linear algebra. The goal of the filtering step is to generate a small, sparse matrix over GF(2), for which one will compute the kernel during the linear algebra step. The filtering step is mainly a structured Gaussian elimination (SGE) over GF(2). For the current factorization records, billions of data are collected in the first step and have to be processed in the filtering step. One part of the filtering step is to remove heavy rows of the matrix. The choice of the weight function to sort heavy rows is critical in order to obtain the smallest matrix possible. In this paper, several weight functions are studied in order to determine which one is more suited in the context of factorization algorithms.

Mots clés: factorization; Number Field Sieve; filtering; structured Gaussian elimination; sparse linear system

Domaines: Cryptographie et sécurité [cs.CR]

Cyril Bouvier. Improvement in the filtering step of integer factorization algorithms. 2012. ⟨hal-00734654v1⟩