[Resource Topic] 2013/388: Parallel Gauss Sieve Algorithm : Solving the SVP in the Ideal Lattice of 128-dimensions

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Title:
Parallel Gauss Sieve Algorithm : Solving the SVP in the Ideal Lattice of 128-dimensions

Authors: Tsukasa Ishiguro, Shinsaku Kiyomoto, Yutaka Miyake, Tsuyoshi Takagi

Abstract:

In this paper, we report that we have solved the SVP Challenge over a 128-dimensional lattice in Ideal Lattice Challenge from TU Darmstadt, which is currently the highest dimension in the challenge that has ever been solved. The security of lattice-based cryptography is based on the hardness of solving the shortest vector problem (SVP) in lattices. In 2010, Micciancio and Voulgaris proposed a Gauss Sieve algorithm for heuristically solving the SVP using a list L of Gauss-reduced vectors. Milde and Schneider proposed a parallel implementation method for the Gauss Sieve algorithm. However, the efficiency of the more than 10 threads in their implementation decreased due to the large number of non-Gauss-reduced vectors appearing in the distributed list of each thread. In this paper, we propose a more practical parallelized Gauss Sieve algorithm. Our algorithm deploys an additional Gauss-reduced list V of sample vectors assigned to each thread, and all vectors in list L remain Gauss-reduced by mutually reducing them using all sample vectors in V. Therefore, our algorithm allows the Gauss Sieve algorithm to run for large dimensions with a small communication overhead. Finally, we succeeded in solving the SVP Challenge over a 128-dimensional ideal lattice generated by the cyclotomic polynomial x^{128}+1 using about 30,000 CPU hours.

ePrint: https://eprint.iacr.org/2013/388

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