A Novel Approximation Algorithm for the Shortest Vector Problem

Finding the shortest vector in a lattice is a NP-hard problem. The best known approximation algorithm for this problem is LLL algorithm with the approximation factor of <inline-formula> <tex-math notation="LaTeX">\alpha ^{\frac {n-1}{2}} </tex-math></inline-formula>...

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Vydané v:IEEE access Ročník 12; s. 141026 - 141031
Hlavný autor: Ajitha Shenoy, K. B.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Piscataway IEEE 2024
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:
Algorithms
Approximation
approximation algorithm
Approximation algorithms
Computational complexity
Indexes
Integer linear programming
Lattice
Lattices
NP-hard problem
Numerical analysis
Object recognition
Polynomials
reduced basis
shortest vector problem
Vectors
ISSN:2169-3536, 2169-3536
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Popis
Shrnutí:Finding the shortest vector in a lattice is a NP-hard problem. The best known approximation algorithm for this problem is LLL algorithm with the approximation factor of <inline-formula> <tex-math notation="LaTeX">\alpha ^{\frac {n-1}{2}} </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">\alpha \geq \frac {4}{3} </tex-math></inline-formula>, which is not a good approximation factor. This work proposes a new polynomial time approximation algorithm for the shortest lattice vector problem. The proposed method makes use of only integer arithmetic and does not require Gram-Schmidt orthogonal basis for generating reduced basis. The proposed method is able to obtain an approximation factor of <inline-formula> <tex-math notation="LaTeX">\frac {1}{(1-\delta)} </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">0 \leq \delta \lt 1 </tex-math></inline-formula>.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2024.3469368