Techniques for Solving Shortest Vector Problem

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The Shortest lattice Vector Problem is central in lattice-based cryptography, as well as in many areas of computational mathematics and computer science, such as computational number theory and combinatorial optimisation. We present an algorithm for solving it in time 2 and space 2, where n is the lattice dimension. This improves the best previously known algorithm, by Micciancio and Voulgaris ...

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Solving the Shortest Lattice Vector Problem in Time 2

The Shortest lattice Vector Problem is central in lattice-based cryptography, as well as in many areas of computational mathematics and computer science, such as computational number theory and combinatorial optimisation. We present an algorithm for solving it in time 2 and space 2, where n is the lattice dimension. This improves the best previously known algorithm, by Micciancio and Voulgaris ...

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Shortest Vector Problem

The Shortest Vector Problem (SVP) is the most famous and widely studied computational problem on lattices. Given a lattice L (typically represented by a basis), SVP asks to find the shortest nonzero vector in L. The problem can be defined with respect to any norm, but the Euclidean norm is the most common (see the entry lattice for a definition). A variant of SVP (commonly studied in computatio...

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The quadratic shortest path problem is the problem of finding a path in a directed graph such that the sum of interaction costs over all pairs of arcs on the path is minimized. We derive several semidefinite programming relaxations for the quadratic shortest path problem with a matrix variable of order m + 1, where m is the number of arcs in the graph. We use the alternating direction method of...

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ژورنال

عنوان ژورنال: International Journal of Advanced Computer Science and Applications

سال: 2021

ISSN: 2156-5570,2158-107X

DOI: 10.14569/ijacsa.2021.0120598