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A Novel Approximation Algorithm for the Shortest Vector Problem
IEEE AccessFinding 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 $\alpha ^{\frac {n-1}{2}}$ , $\alpha \geq \frac {4}{3}$ , which is not a good ...
K. B. Ajitha Shenoy
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Sieve algorithms for the shortest vector problem are practical [PDF]
Journal of Mathematical Cryptology, 2008 The most famous lattice problem is the Shortest Vector Problem (SVP), which has many applications in cryptology. The best approximation algorithms known for SVP in high dimension rely on a subroutine for exact SVP in low dimension.
Nguyen Phong Q., Vidick Thomas
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Improved hardness results for unique shortest vector problem [PDF]
Information Processing Letters, 2016 We give several improvements on the known hardness of the unique shortest vector problem. - We give a deterministic reduction from the shortest vector problem to the unique shortest vector problem. As a byproduct, we get deterministic NP-hardness for unique shortest vector problem in the $\ell_\infty$ norm.
Aggarwal, Divesh, Dubey, Chandan
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Improved algorithms for the Shortest Vector Problem and the Closest Vector Problem in the infinity norm [PDF]
, 2018 Changed the ...
Divesh Aggarwal, Priyanka Mukhopadhyay
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Explicit Hard Instances of the Shortest Vector Problem [PDF]
IACR Cryptol. ePrint Arch., 2008 Building upon a famous result due to Ajtai, we propose a sequence of lattice bases with growing dimension, which can be expected to be hard instances of the shortest vector problem ( SVP ) and which can therefore be used to benchmark lattice reduction algorithms. The SVP is the basis of security for potentially post-quantum cryptosystems.
Johannes Buchmann 0001 +2 more
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On the Ideal Shortest Vector Problem over Random Rational Primes [PDF]
, 2021 Any ideal in a number field can be factored into a product of prime ideals. In this paper we study the prime ideal shortest vector problem (SVP) in the ring $ \Z[x]/(x^{2^n} + 1) $, a popular choice in the design of ideal lattice based cryptosystems. We show that a majority of rational primes lie under prime ideals admitting a polynomial time algorithm
Yanbin Pan +3 more
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The nc-Unique Shortest Vector Problem is Hard. [PDF]
IACR Cryptol. ePrint Arch., 2008 The unique Shortest Vector Problem (uSVP) gained prominence because it was the problem upon which the first provably-secure lattice-based cryptosystems were built.
Vadim Lyubashevsky
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Heuristic Time Complexity of NISQ Shortest-Vector-Problem Solvers
IEEE Transactions on Quantum EngineeringThe shortest vector problem (SVP) is central to the security of lattice-based cryptography, forming the foundation of two of the three NIST-standardized postquantum cryptosystems. Understanding how quantum algorithms perform on SVP is vital for assessing
Milos Prokop, Petros Wallden
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On the hardness of the shortest vector problem. [PDF]
, 1998 An n-dimensional lattice is the set of all integral linear combinations of n linearly independent vectors in Rm. One of the most studied algorithmic problems on lattices is the shortest vector problem (SVP): given a lattice, find the shortest non-zero vector in it.
Micciancio, Daniele, Daniele Micciancio
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Techniques for Solving Shortest Vector Problem [PDF]
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.
V. Dinesh Reddy +4 more
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