Conference Paper
Some Sieving Algorithms for Lattice Problems.
DOI: 10.4230/LIPIcs.FSTTCS.2008.1738 Conference: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2008, December 911, 2008, Bangalore, India
Source: DBLP
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 "In 2001 Ajtai et al. proposed the first sieve algorithm for solving the SVP [3]. There are many variants of the sieving algorithm [22, 6, 5] that try to improve the computational costs of the algorithm. In 2009 Micciancio and Voulgaris proposed a practical sieving algorithm, called the Gauss Sieve algorithm [20]. "
Article: Parallel Gauss Sieve Algorithm: Solving the SVP Challenge over a 128Dimensional Ideal Lattice
[Show abstract] [Hide abstract] ABSTRACT: In this paper, we report that we have solved the SVP Challenge over a 128dimensional 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 latticebased 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 Gaussreduced 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 nonGaussreduced 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 Gaussreduced list V of sample vectors assigned to each thread, and all vectors in list L remain Gaussreduced 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 128dimensional ideal lattice generated by the cyclotomic polynomial x 128 + 1 using about 30,000 CPU hours. 
 "These problems are central to the geometry of numbers and have applications to integer programming, factoring polynomials, cryptography etc. The fastest known algorithms for solving SVP in general norms, are 2 O(n) time randomized algorithms based on the AKS sieve [1, 2]. Finding deterministic algorithms of this complexity for both SVP and CVP has been an important open problem. "
[Show abstract] [Hide abstract] ABSTRACT: We give a deterministic 2(o(n))algorithm for computing an Mellipsoid of a convex body, matching a known lower bound. This leads to a nearly optimal deterministic algorithm for estimating the volume of a convex body and improved deterministic algorithms for fundamental lattice problems under general norms. 