Parallel gauss sieve algorithm: Solving the SVP challenge over a 128-dimensional ideal lattice

Tsukasa Ishiguro, Shinsaku Kiyomoto, Yutaka Miyake, Tsuyoshi Takagi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

20 Citations (Scopus)

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 x128+1 using about 30,000 CPU hours.

Original languageEnglish
Title of host publicationPublic-Key Cryptography, PKC 2014 - 17th International Conference on Practice and Theory in Public-Key Cryptography, Proceedings
PublisherSpringer Verlag
Pages411-428
Number of pages18
ISBN (Print)9783642546303
DOIs
Publication statusPublished - Jan 1 2014
Event17th IACR International Conference on Practice and Theory in Public-Key Cryptography, PKC 2014 - Buenos Aires, Argentina
Duration: Mar 26 2014Mar 28 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8383 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other17th IACR International Conference on Practice and Theory in Public-Key Cryptography, PKC 2014
CountryArgentina
CityBuenos Aires
Period3/26/143/28/14

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All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Ishiguro, T., Kiyomoto, S., Miyake, Y., & Takagi, T. (2014). Parallel gauss sieve algorithm: Solving the SVP challenge over a 128-dimensional ideal lattice. In Public-Key Cryptography, PKC 2014 - 17th International Conference on Practice and Theory in Public-Key Cryptography, Proceedings (pp. 411-428). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8383 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-642-54631-0_24