The complexity analysis relies on the Gaussian heuristic. This heuristic is backed by experiments in low and high dimensions that closely reflect these estimates when solving hard lattice problems in the average case. This new approach allows us to solve not only shortest vector problems, but also...
This paper shows that upper bounds on the coefficients of the shortest vector of a lattice can be represented using the smallest eigenvalue of the Gram matrix for the lattice, obtains its distribution for high-dimensional random Goldstein-Mayer lattice, and applies it to determine the percentage ...
The complexity analysis relies on the Gaussian heuristic. This heuristic is backed by experiments in low and high dimensions that closely reflect these estimates when solving hard lattice problems in the average case. This new approach allows us to solve not only shortest vector problems, but also...
motivated by the construction of analogous combinatorial objects over integer lattices, which are used in NP-hardness proofs for the Shortest Vector Problem ... Micciancio,Daniele - Computational Complexity 被引量: 6发表: 2014年 Locally Dense Codes (e.g., Reed-Solomon codes concatenated with Hadama...
We initiate the study of the computational complexity of the covering radius problem for lattices, and approximation versions of the problem for both lattices and linear codes. We also investigate the computational complexity of the shortest linearly independent vectors problem, and its relation to the...
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 ...
Computational complexity Lattices Shortest vector problem Approximation algorithms Hardness of approximation View PDFReferences [1] D. Aharonov, O. Regev, Lattice problems in NP ∩ coNP, in: Proceedings of the 45th IEEE Symposium on Foundations of Computer Science, 2004, pp. 362–371. Google Schol...
The Effect of Preprocessing to the Complexity of List Sphere Detector Algorithms M Myllylae,M Juntti,J Cavallaro 被引量: 0发表: 2022年 The hardness of decoding linear codes with preprocessing The problem of maximum-likelihood decoding of linear block codes is known to be hard. The fact that ...
We focus on the recent progress on complexity results of intractability. We will discuss Ajtai’s worst-case/average-case connections for the shortest vector problem, similar results for the closest vector problem and short basis problem, NP-hardness and non-NP-hardness, transference theorems ...
Summary: In 2009, Bl枚mer and Naewe proposed the Generalized Shortest Vector Problem $(ext {GSVP})$. We initiate the study of the promise problem ($ext {GAPSAM}$) for $ext {GSVP}$. It is a promise problem associated with estimating the subspace avoiding minimum. We show $ext {GAP...