We prove a connection of the worst-case complexity to the average-case complexity based on the Closest Vector Problem (CVP) for lattices. Assume that there is an efficient algorithm which can solve approximately a random instance of CVP, with a non-trivial success probability, for lattices under a certain natural distribution, we show that one can approximately solve several lattice problems (i...

Let S be a set of k strings over an alphabet Σ; each string has a length between ` and n. The Closest Substring Problem (CSSP) is to find a minimal integer d (and a corresponding string t of length `) such that each string s ∈ S has a substring of length ` with Hamming distance at most d to t. We say t is the closest substring to S. For ` = n, this problem is known as the Closest String Problem...

The paper is a comparative study of major modeling and pattern discovery approaches applicable to the area of Bioinformatics and the area of decision support systems in general. These approaches include inductive versus transductive reasoning, global, local, and personalized modeling and their potentials are illustrated on a case study of gene expression and clinical data related to cancer outc...

Computing a shortest nonzero vector of a given euclidean lattice and computing a closest lattice vector to a given target are pervasive problems in computer science, computational mathematics and communication theory. The classical algorithms for these tasks were invented by Ravi Kannan in 1983 and, though remarkably simple to establish, their complexity bounds have not been improved for almost...

The area of lattice-based cryptography is growing ever-more prominent as a paradigm for quantum-resistant cryptography. One of the most important hard problem underpinning the security of latticebased cryptosystems is the shortest vector problem (SVP). At present, two approaches dominate methods for solving instances of this problem in practice: enumeration and sieving. In 2010, Micciancio and ...

The picture quality of conventional memory vector quantization techniques is limited by their supercodebooks. This paper presents a new dynamic finite-state vector quantization (DFSVQ) algorithm which provides better quality than the best quality that the supercodebook can offer. The new DFSVQ exploits the global interblock correlation of image blocks instead of local correlation in conventiona...

GPU voxel-based surface ray-casting has positioned as an interesting alternative to rasterization-based rendering approaches, because it allows using many processing units simultaneously, can effectively exploit thread level parallelism, and enables fine-granularity occlusion culling on the pixel level. Yet voxel-based techniques face the problem that an extremely high resolution is necessary t...

In this paper, we present a heuristic algorithm for solving exact, as well as approximate, SVP and CVP for lattices. This algorithm is based on a new approach which is very different from and complementary to the sieving technique. This new approach frees us from the kissing number bound and allows us to solve SVP and CVP in lattices of dimension n in time 2 using memory 2. The key idea is to n...

This is a chapter from version 1.1 of the book “Mathematics of Public Key Cryptography” by Steven Galbraith, available from http://www.isg.rhul.ac.uk/̃ sdg/crypto-book/ The copyright for this chapter is held by Steven Galbraith. This book is now completed and an edited version of it will be published by Cambridge University Press in early 2012. Some of the Theorem/Lemma/Exercise numbers may be d...

Abstract. The security of lattice-based cryptosystems such as NTRU, GGH and Ajtai-Dwork essentially relies upon the intractability of computing a shortest non-zero lattice vector and a closest lattice vector to a given target vector in high dimensions. The best algorithms for these tasks are due to Kannan, and, though remarkably simple, their complexity estimates have not been improved since ov...