scholarly journals An Efficient Algorithm for the Shortest Vector Problem

IEEE Access ◽  
2018 ◽  
Vol 6 ◽  
pp. 61478-61487 ◽  
Author(s):  
Yu-Lun Chuang ◽  
Chun-I Fan ◽  
Yi-Fan Tseng
Keyword(s):  
Efficient Algorithm ◽  
Vector Problem ◽  
Shortest Vector Problem

scholarly journals Space-efficient classical and quantum algorithms for the shortest vector problem

2018 ◽  
Vol 18 (3&4) ◽  
pp. 283-305
Author(s):  
Yanlin Chen ◽  
Kai-Min Chung ◽  
Ching-Yi Lai
Keyword(s):  
Efficient Algorithm ◽  
Coding Theory ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Nonzero Vector ◽  
Vector Problem ◽  
Shortest Vector Problem ◽  
Linearly Independent ◽  
Classical Algorithm ◽  
Quantum Version

A lattice is the integer span of some linearly independent vectors. Lattice problems have many significant applications in coding theory and cryptographic systems for their conjectured hardness. The Shortest Vector Problem (SVP), which asks to find a shortest nonzero vector in a lattice, is one of the well-known problems that are believed to be hard to solve, even with a quantum computer. In this paper we propose space-efficient classical and quantum algorithms for solving SVP. Currently the best time-efficient algorithm for solving SVP takes 2^{n+o(n)} time and 2^{n+o(n)} space. Our classical algorithm takes 2^{2.05n+o(n)} time to solve SVP and it requires only 2^{0.5n+o(n)} space. We then adapt our classical algorithm to a quantum version, which can solve SVP in time 2^{1.2553n+o(n)} with 2^{0.5n+o(n)} classical space and only poly(n) qubits.

An Efficient Algorithm for Optimally Solving a Shortest Vector Problem in Compute-and-Forward Design

2016 ◽  
Vol 15 (10) ◽  
pp. 6541-6555 ◽  
Author(s):  
Jinming Wen ◽  
Baojian Zhou ◽  
Wai Ho Mow ◽  
Xiao-Wen Chang
Keyword(s):  
Efficient Algorithm ◽  
Vector Problem ◽  
Shortest Vector Problem
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