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Solving the Shortest Vector Problem in Lattices Faster Using Quantum Search

  • Thijs Laarhoven
  • Michele Mosca
  • Joop van de Pol
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7932)

Abstract

By applying Grover’s quantum search algorithm to the lattice algorithms of Micciancio and Voulgaris, Nguyen and Vidick, Wang et al., and Pujol and Stehlé, we obtain improved asymptotic quantum results for solving the shortest vector problem. With quantum computers we can provably find a shortest vector in time 21.799n + o(n), improving upon the classical time complexity of 22.465n + o(n) of Pujol and Stehlé and the 22n + o(n) of Micciancio and Voulgaris, while heuristically we expect to find a shortest vector in time 20.312n + o(n), improving upon the classical time complexity of 20.384n + o(n) of Wang et al. These quantum complexities will be an important guide for the selection of parameters for post-quantum cryptosystems based on the hardness of the shortest vector problem.

Keywords

lattices shortest vector problem sieving quantum algorithms quantum search 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Thijs Laarhoven
    • 1
  • Michele Mosca
    • 2
    • 3
  • Joop van de Pol
    • 4
  1. 1.Dept. of Mathematics and Computer ScienceEindhoven University of TechnologyNetherlands
  2. 2.Institute for Quantum Computing and Dept. of C&OUniversity of WaterlooCanada
  3. 3.Perimeter Institute for Theoretical PhysicsCanada
  4. 4.Dept. of Computer ScienceUniversity of BristolUK

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