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Parameterized Intractability of Even Set and Shortest Vector Problem [PDF]

Journal of the ACM, 2021
The -Even Set problem is a parameterized variant of the Minimum Distance Problem of linear codes over
Karthik C S, Pasin Manurangsi, Édouard Bonnet   +2 more
exaly   +7 more sources

A Three-Level Sieve Algorithm for the Shortest Vector Problem [PDF]

Lecture Notes in Computer Science, 2014
In AsiaCCS 2011, Wang et al. proposed a two-level heuristic sieve algorithm for the shortest vector problem in lattices, which improves the Nguyen-Vidick sieve algorithm. Inspired by their idea, we present a three-level sieve algorithm in this paper, which is shown to have better time complexity. More precisely, the time complexity of our algorithm is
Yanbin Pan
exaly   +6 more sources

On the Unique Shortest Lattice Vector Problem

Theoretical Computer Science, 2001
We show that the problem of deciding whether a given rational lattice \(L\) has a vector of length less than some given value \(r\) is NP-hard, even under the promise that \(L\) has exactly zero or one vector of length less than \(r\).
D Sivakumar
exaly   +3 more sources

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The Complexity of the Shortest Vector Problem

ACM SIGACT News, 2023
Computational problems on point lattices play a central role in many areas of computer science including integer programming, coding theory, cryptanalysis, and especially the design of secure cryptosystems. In this survey, we present known results and open questions related to the complexity of the most important of these problems, the Shortest Vector ...
openaire   +2 more sources

On Promise Problem of the Generalized Shortest Vector Problem

Lecture Notes in Computer Science, 2016
In 2009, Blomer and Naewe proposed the Generalized Shortest Vector Problem \((\text {GSVP})\). We initiate the study of the promise problem (\(\text {GAPSAM}\)) for \(\text {GSVP}\). It is a promise problem associated with estimating the subspace avoiding minimum. We show \(\text {GAPSAM}_{c\cdot n}\) lies in coNP, where c is a constant.
Wenwen Wang, Kewei Lv
exaly   +3 more sources

A note on the shortest lattice vector problem

Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317), 2003
We show that the problem of deciding whether a given rational lattice L has a vector of length less than some given value r is NP-hard under randomized reductions, even under the promise that L has exactly zero or one vector of length less than r.
Ravi Kumar 0001, D. Sivakumar 0001
openaire   +2 more sources

Shortest Vector Problem

2002
In this chapter we study the hardness of approximating the shortest vector problem (SVP). Recall that in SVP one is given a matrix \( B \in {\mathbb{Q}^{{m \times n}}} \), and the goal is to find the shortest nonzero vector in the lattice generated by B .
Daniele Micciancio, Shafi Goldwasser
openaire   +1 more source

A sieve algorithm for the shortest lattice vector problem

Proceedings of the thirty-third annual ACM symposium on Theory of computing, 2001
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 ...
Miklós Ajtai, Ravi Kumar 0001, D. Sivakumar 0001   +2 more
openaire   +1 more source