Resolution of Linear Algebra for the Discrete Logarithm Problem Using GPU and Multi-core Architectures
This work addresses cryptanalysis challenges for security assessment of public-key cryptosystems, but is incremental as it applies existing methods to new hardware setups.
The paper tackles solving large sparse linear systems for discrete logarithm problems by implementing parallel algorithms on GPU and multi-core clusters with InfiniBand networking, achieving a record-sized computation in GF(2^809).
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($2^{809}$).