# Resolution of Linear Algebra for the Discrete Logarithm Problem using GPU and Multi-core Architectures

1 CARAMEL - Cryptology, Arithmetic: Hardware and Software
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : 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 GPU- and multi-core-based clusters, featuring InfiniBand networking. More specifically, we present the sparse linear algebra algorithms that are proposed in the literature, in particular the block Wiedemann algorithm. We discuss the parallelization of the central matrix--vector product operation from both algorithmic and practical points of view, and illustrate how our approach has contributed to the recent record-sized DLP computation in GF($2^{809}$).
keyword :
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.inria.fr/hal-00946895
Contributor : Hamza Jeljeli Connect in order to contact the contributor
Submitted on : Friday, February 14, 2014 - 5:20:08 PM
Last modification on : Saturday, October 16, 2021 - 11:26:06 AM
Long-term archiving on: : Thursday, May 15, 2014 - 5:02:44 AM

### Files

linalg.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-00946895, version 1
• ARXIV : 1402.3661

### Citation

Hamza Jeljeli. Resolution of Linear Algebra for the Discrete Logarithm Problem using GPU and Multi-core Architectures. 2014. ⟨hal-00946895v1⟩

### Metrics

Les métriques sont temporairement indisponibles