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ALMOST PERFECT LATTICES, THE COVERING RADIUS PROBLEM, AND APPLICATIONS TO AJTAI'S CONNECTION FACTOR.

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Bibliographic Details
Title: ALMOST PERFECT LATTICES, THE COVERING RADIUS PROBLEM, AND APPLICATIONS TO AJTAI'S CONNECTION FACTOR.
Source: SIAM Journal on Computing; 2004, Vol. 34 Issue 1, p118-169, 52p
Subject Terms: LATTICE theory, NUMERICAL calculations, CRYPTOGRAPHY, MATHEMATICS, RADIUS (Geometry), ABSTRACT algebra, PHONOLOGICAL decoding, CONVEX bodies
People: AJTAI, Miklos
Abstract: The article focuses on lattices as a potential source of computational hardness. It is stated that lattices are used in cryptography, after a breakthrough result of Ajtai, connecting the average-case and worst-case complexity of several lattice problems. It presents a self-contained proof of results along the line of Miklos Ajtai's seminal work and explores the possibility of quantitative improvement in Ajtai's original results. It also presents several lattice problems related to the covering radius, the bounded distance decoding problem and approximate counting of lattice points inside convex bodies.
Database: Complementary Index
Description
Abstract:The article focuses on lattices as a potential source of computational hardness. It is stated that lattices are used in cryptography, after a breakthrough result of Ajtai, connecting the average-case and worst-case complexity of several lattice problems. It presents a self-contained proof of results along the line of Miklos Ajtai's seminal work and explores the possibility of quantitative improvement in Ajtai's original results. It also presents several lattice problems related to the covering radius, the bounded distance decoding problem and approximate counting of lattice points inside convex bodies.
ISSN:00975397
DOI:10.1137/S0097539703433511