Finding shortest lattice vectors faster using quantum search

T.M.M. Laarhoven, Michele Mosca, Joop Pol, van de

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By applying a quantum search algorithm to various heuristic and provable sieve algorithms from the literature, we obtain improved asymptotic quantum results for solving the shortest vector problem on lattices. With quantum computers we can provably find a shortest vector in time $2^{1.799n + o(n)}$, improving upon the classical time complexities of $2^{2.465n + o(n)}$ of Pujol and Stehl\'{e} and the $2^{2n + o(n)}$ of Micciancio and Voulgaris, while heuristically we expect to find a shortest vector in time $2^{0.286n + o(n)}$, improving upon the classical time complexity of $2^{0.337n + o(n)}$ of Laarhoven. 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 search
Originele taal-2Engels
Aantal pagina's26
StatusGepubliceerd - 2014

Publicatie series

NaamCryptology ePrint Archive
Volume2014/907

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