An Accelerated Algorithm for Solving SVP Based on Statistical Analysis (original) (raw)
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Techniques for Solving Shortest Vector Problem
International Journal of Advanced Computer Science and Applications, 2021
Lattice-based crypto systems are regarded as secure and believed to be secure even against quantum computers. lattice-based cryptography relies upon problems like the Shortest Vector Problem. Shortest Vector Problem is an instance of lattice problems that are used as a basis for secure cryptographic schemes. For more than 30 years now, the Shortest Vector Problem has been at the heart of a thriving research field and finding a new efficient algorithm turned out to be out of reach. This problem has a great many applications such as optimization, communication theory, cryptography, etc. This paper introduces the Shortest Vector Problem and other related problems such as the Closest Vector Problem. We present the average case and worst case hardness results for the Shortest Vector Problem. Further this work explore efficient algorithms solving the Shortest Vector Problem and present their efficiency. More precisely, this paper presents four algorithms: the Lenstra-Lenstra-Lovasz (LLL) ...
Iran Journal of Computer Science
The shortest vector problem (SVP) is absolutely essential in lattice-based cryptography. In this paper, we significantly improve genetic algorithms (GAs) for solving the SVP. GAs, which are simple and powerful optimization techniques, that have the potential to eliminate the limitations of the existing fast SVP algorithms. We improve the entire phase of the GA construction. Our proposed method is based on the concept of low memory consumption and high reproducibility, and this is the main and significant difference between our algorithm and the other SVP algorithms. Our contributions are twofold. First, we developed a new GA for solving the SVP and achieved a considerable improvement in the running time performance. Second, we interpreted certain genetic operations, such as mutation and crossover, in the context of lattices, which has not been done in previous studies. The general result of this paper is that we showed the potential of GAs in the field of lattices.
A sieve algorithm for the shortest lattice vector problem
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Abstract We present a randomized 2^{O (n)} time algorithm to compute a shortest non-zero vector in an n-dimensional rational lattice. The best known time upper bound for this problem was 2^{O (n\ log n)} first given by Kannan [7] in 1983. We obtain several consequences of this algorithm for related problems on lattices and codes, including an improvement for polynomial time approximations to the shortest vector problem. In this improvement we gain a factor of log log n in the exponent of the approximating factor.
Sampling short lattice vectors and the closest lattice vector problem
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Abstract We present a 2 O (n) time Turing reduction from the closest lattice vector problem to the shortest lattice vector problem. Our reduction assumes access to a subroutine that solves SVP exactly and a subroutine to sample short vectors from a lattice, and computes a (1+ ε)-approximation to CVP As a consequence, using the SVP algorithm from (Ajtai et al., 2001), we obtain a randomized 2 [O (1+ ε-1) n] algorithm to obtain a (1+ ε)-approximation for the closest lattice vector problem in n dimensions.
A Heuristic Method to Approximate the Closest Vector Problem
WSEAS TRANSACTIONS ON MATHEMATICS, 2022
The closest vector problem, or CVP for short, is a fundamental lattice problem. The purpose of this challenge is to identify a lattice point in its ambient space that is closest to a given point. This is a provably hard problem to solve, as it is an NP-hard problem. It is considered to be more difficult than the shortest vector problem (SVP), in which the shortest nonzero lattice point is required. There are three types of algorithms that can be used to solve CVP: Enumeration algorithms, Voronoi cell computation and seiving algorithms. Many algorithms for solving the relaxed variant, APPROX-CVP, have been proposed: The Babai nearest algorithm or the embedding technique. In this work we will give a heuristic method to approximate the closest vector problem to a given vector using the embeding technique and the reduced centered law.