Faster Sieving Algorithm for Approximate SVP with Constant ...

We also explain why these improvements carry over to also give the fastest quantum algorithms for the approximate shortest vector problem. 1 Introduction. A ...

Abstract. There is a large gap between theory and practice in the complexities of sieving algorithms for solving the shortest vector problem in an arbitrary ...

Faster Sieving Algorithm for Approximate SVP with Constant ...

Faster Sieving Algorithm for Approximate SVP with Constant Approximation Factors. Resource URI: https://dblp.l3s.de/d2r/resource/publications/journals/iacr ...

Faster Provable Sieving Algorithms for the Shortest Vector Problem ...

Micciancio [52] showed that SVP is NP-hard to approximate within some constant approximation factor. Subsequently, it was shown that ...

Lecture 8 2O(n) -time algorithm for SVP

... algorithm that approximates the SVP to within nc for some constant c. Its ... A sieve algorithm for the shortest lattice vector problem. In. Proc. 33rd ...

(PDF) The faster lattice sieving for SVP - ResearchGate

There are many famous heuristic lattice sieving algorithms to solve SVP, such as the Gauss Sieve, NV Sieve, which deal the full-rank n - ...

Sieving Algorithms for Exact SVP 1 Background 2 List ... - UCSD CSE

For example, earlier in the course we saw how solving SVP in lower dimensions is critical for performing BKZ lattice reduction quickly. This lecture focuses on ...

Faster Provable Sieving Algorithms for the Shortest Vector Problem ...

In this work, we give provable sieving algorithms for the Shortest Vector Problem (SVP) and the Closest Vector Problem (CVP) on lattices in ℓp norm (1≤p≤∞).

Provable Sieving Algorithms for the Shortest Vector Problem and the ...

Euclidean norm. ▷ Ajtai,Kumar,Sivakumar(20001, 20022) solved SVP and approximate CVP in 2cn time using randomized sieving. ▷ Fastest algorithm3 for SVPc ...

Sieving Algorithms for Lattice Problems - Computer Science

... algorithm that can solve approximate 2n/2-SVP. This is not a very strict ... problem solver, it is still the fastest polynomial space algorithm for solving SVP/ ...

Provable Sieving Algorithms for SVP and CVP in the l_p norm

Priyanka Mukhopadhyay, University of Waterloo https://simons.berkeley.edu/talks/provable-sieving-algorithms-svp-and-cvp-lp-norm-0 Lattices: ...

Faster exponential time algorithms for the shortest vector problem

The asymptotically fastest known algorithm for SVP (namely, the AKS Sieve introduced by ... A similar situation ex- ists in the context of approximation ...

Sieve Algorithms for the Shortest Vector Problem are Practical

The best approximation algorithms known for SVP in high dimension rely on a subroutine for exact SVP in low dimension. In this paper, we assess the practicality ...

A Sieve Algorithm for the Shortest Lattice Vector Problem - CiteSeerX

Note that if the basic algorithm stops with a non-zero wi, we already have a constant factor approximation algorithm for SVP. To ensure that wi is non-zero and ...

Approximate CVPp in time 20.802n - ScienceDirect

Blömer and Naewe [14] extended the randomized sieving algorithm of Ajtai et al. to solve SVP p and obtain a 2 O ( n ) time and space exact algorithm for SVP p ...

The Complexity of the Shortest Vector Problem

to average-case reductions reduce from approximate search SVP on ideal lattices. ... Fast factoring integers by SVP algorithms. IACR Cryptol.

arXiv:1607.04789v1 [cs.CR] 16 Jul 2016

Keywords: lattices, sieving algorithms, approximate nearest neighbors, shortest vector problem (SVP), closest vector problem (CVP), bounded ...

Fine-grained hardness of lattice problems: Open questions

... algorithm for CVP immediately gives an essentially equally fast algorithm for SVP. ... (For SVP and for constant-factor approximate CVP, 2^{O(n)}- ...

Faster exponential time algorithms for the shortest vector problem.

... We now describe our main contribution. As we mentioned already, SVP 2 can be approximated up to a constant factor in time 2 (0.802+ε) ...

Faster provable sieving algorithms for the Shortest Vector Problem ...

this paper we give provable sieving algorithms for the Shortest Vector Problem (SVP) ... 2020. We show that a constant factor approximation of the shortest and ...