# 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($2^{809}$).
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Type de document :
Communication dans un congrès
Euro-Par 2014 Parallel Processing, Aug 2014, Porto, Portugal. 〈http://europar2014.dcc.fc.up.pt/〉
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Littérature citée [23 références]

https://hal.inria.fr/hal-00946895
Contributeur : Hamza Jeljeli <>
Soumis le : jeudi 11 décembre 2014 - 13:38:32
Dernière modification le : jeudi 11 janvier 2018 - 06:23:16
Document(s) archivé(s) le : jeudi 12 mars 2015 - 10:41:26

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linalg.pdf
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• HAL Id : hal-00946895, version 3
• ARXIV : 1402.3661

### Citation

Hamza Jeljeli. Resolution of Linear Algebra for the Discrete Logarithm Problem Using GPU and Multi-core Architectures. Euro-Par 2014 Parallel Processing, Aug 2014, Porto, Portugal. 〈http://europar2014.dcc.fc.up.pt/〉. 〈hal-00946895v3〉

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