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A Simulated Annealing Algorithm for SVP Challenge Through y-Sparse Representations of Short Lattice Vectors

  • Dan DingEmail author
  • Guizhen Zhu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9473)

Abstract

In this paper, we propose a novel simulated annealing algorithm for the shortest vector problem through y-sparse representations of short lattice vectors. A Markov analysis proves that the algorithm guarantees to converge to the shortest vector at a probability 1, under certain conditions to ensure strong ergodicity of its inhomogeneous Markov chain. After that, we propose a polynomial-time approximation version of our algorithm, and the experimental results under benchmarks in SVP challenge [27] show that the simulated annealing one outperforms the famous Kannan’s algorithm in two aspects: it runs exponentially faster and it succeeds in searching the shortest vectors in lattices of higher dimensions. Therefore, our newly-proposed algorithm is a fast and efficient SVP solver and paves a completely new road for SVP algorithms.

Keywords

Lattice-based cryptography Simulated annealing Shortest vector problem Inhomogeneous markov chain Strong ergodicity 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Computer Science and TechnologyTsinghua UniversityBeijingChina
  2. 2.Data Communication Science and Technology Research InstituteBeijingChina

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