Solving the Shortest Vector Problem in Lattices Faster Using Quantum Search

被引：0
|
作者：
Laarhoven, Thijs [1 ]
Mosca, Michele [2 ,3 ]
van de Pol, Joop [4 ]
机构：
[1] Eindhoven Univ Technol, Dept Math & Comp Sci, NL-5600 MB Eindhoven, Netherlands
[2] Univ Waterloo, Inst Quantum Comp, Dept C&O, Waterloo, ON N2L 3GL, Canada
[3] Univ Waterloo, Perimeter Inst Theoret Phys, Waterloo, ON N2L 2Y5, Canada
[4] Univ Bristol, Dept Comp Sci, Bristol BS81UB, Avon, England
来源：
POST-QUANTUM CRYPTOGRAPHY, PQCRYPTO 2013 | 2013年 / 7932卷
基金：
英国工程与自然科学研究理事会; 加拿大自然科学与工程研究理事会;
关键词：
lattices; shortest vector problem; sieving; quantum algorithms; quantum search; BASIS REDUCTION; ALGORITHMS; ENUMERATION;
D O I：
暂无
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
By applying Grover's quantum search algorithm to the lattice algorithms of Micciancio and Voulgaris, Nguyen and Vidick, Wang et al., and Pujol and Stehle, we obtain improved asymptotic quantum results for solving the shortest vector problem. With quantum computers we can provably find a shortest vector in time 2(1.799n+o(n)), improving upon the classical time complexity of 2(2.465n+o(n)) of Pujol and Stehle and the 2(2n+o(n)) of Micciancio and Voulgaris, while heuristically we expect to find a shortest vector in time 2(0.312n+o(n)), improving upon the classical time complexity of 2(0.384n+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.
引用
收藏
页码：83 / 101
页数：19
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