Solving Homogeneous Linear Equations over Gf(2) via Block Wiedemann Algorithm
نویسنده
چکیده
We propose a method of solving large sparse systems of homogeneous linear equations over GF(2), the field with two elements. We modify an algorithm due to Wiedemann. A block version of the algorithm allows us to perform 32 matrix-vector operations for the cost of one. The resulting algorithm is competitive with structured Gaussian elimination in terms of time and has much lower space requirements. It may be useful in the last stage of integer factorization.
منابع مشابه
Algorithms for Solving Linear and Polynomial Systems of Equations over Finite Fields with Applications to Cryptanalysis
Title of dissertation: ALGORITHMS FOR SOLVING LINEAR AND POLYNOMIAL SYSTEMS OF EQUATIONS OVER FINITE FIELDS WITH APPLICATIONS TO CRYPTANALYSIS Gregory Bard Doctor of Philosophy, 2007 Dissertation directed by: Professor Lawrence C. Washington Department of Mathematics This dissertation contains algorithms for solving linear and polynomial systems of equations over GF(2). The objective is to prov...
متن کاملResolution of Linear Algebra for the Discrete Logarithm Problem Using GPU and Multi-core Architectures
In cryptanalysis, solving the discrete logarithm problem (DLP) is key to assessing the security of many public-key cryptosystems. The index-calculus methods, that attack the DLP in multiplicative subgroups of finite fields, require solving large sparse systems of linear equations modulo large primes. This article deals with how we can run this computation on GPUand multi-core-based clusters, fe...
متن کاملA Study of Coppersmith ' S Block Wiedemannalgorithm Using Matrix Polynomialsgilles
Nous analysons un algorithme probabiliste par blocs, propos e par Coppersmith, pour la r esolution de grands syst emes lin eaires creux Aw = 0 donn es sur un corps ni K =GF(q). Cet algorithme est une modiication d'un algorithme de Wiedemann. Coppersmith a justii e sa m ethode par plusieurs arguments heuristiques. Une question ouverte etait de d emontrer que l'algorithme peut eeectivement fourni...
متن کاملAlgorithmic algebraic techniques and their application to block cipher cryptanalysis
In Part I we present and discuss implementations of both well-known and novel algorithms for fundamental problems of linear algebra over the field with two elements GF(2). In particular, we present the best known implementations for matrix-matrix multiplication and matrix decomposition for dense matrices over GF(2). These implementations are based on novel variants of the “M4RM” multiplication ...
متن کاملAccelerating Iterative SpMV for Discrete Logarithm Problem using GPUs
In the context of cryptanalysis, computing discrete logarithms in large cyclic groups using index-calculus-based methods, such as the number field sieve or the function field sieve, 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 — itera...
متن کامل