Improving BDD Enumeration for LWE Problem Using GPU

Esseissah, Mohamed S.; Bhery, Ashraf; Bahig, Hatem M.

doi:10.1109/access.2019.2961091

Cited by 3 publications

(1 citation statement)

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“…e second strategy is based on expecting the best level α on which the cost of transferring the data between CPU and GPU is very low, while the third strategy is based on gaining the improvement based on GPU, which can be carried out by generating some subtrees in GPU rather than in CPU. e main idea of the third strategy is similar to another one used for improving BDD Enumeration [33].…”

Section: Our Contributionmentioning

confidence: 99%

Three Strategies for Improving Shortest Vector Enumeration Using GPUs

Esseissah

Bhery

Daoud

et al. 2021

Scientific Programming

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Hard Lattice problems are assumed to be one of the most promising problems for generating cryptosystems that are secure in quantum computing. The shortest vector problem (SVP) is one of the most famous lattice problems. In this paper, we present three improvements on GPU-based parallel algorithms for solving SVP using the classical enumeration and pruned enumeration. There are two improvements for preprocessing: we use a combination of randomization and the Gaussian heuristic to expect a better basis that leads rapidly to a shortest vector and we expect the level on which the exchanging data between CPU and GPU is optimized. In the third improvement, we improve GPU-based implementation by generating some points in GPU rather than in CPU. We used NVIDIA GeForce GPUs of type GTX 1060 6G. We achieved a significant improvement upon Hermans’s improvement. The improvements speed up the pruned enumeration by a factor of almost 2.5 using a single GPU. Additionally, we provided an implementation for multi-GPUs by using two GPUs. The results showed that our algorithm of enumeration is scalable since the speedups achieved using two GPUs are almost faster than Hermans’s improvement by a factor of almost 5. The improvements also provided a high speedup for the classical enumeration. The speedup achieved using our improvements and two GPUs on a challenge of dimension 60 is almost faster by factor 2 than Correia’s parallel implementation using a dual-socket machine with 16 physical cores and simultaneous multithreading technology.

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Section: Our Contributionmentioning

confidence: 99%