Complexity of Lattice Problems: A Cryptographic Perspective Daniele Micciancio

ISBN: 9780792376880

Published: March 31st 2002

Hardcover

220 pages


Description

Complexity of Lattice Problems: A Cryptographic Perspective  by  Daniele Micciancio

Complexity of Lattice Problems: A Cryptographic Perspective by Daniele Micciancio
March 31st 2002 | Hardcover | PDF, EPUB, FB2, DjVu, audiobook, mp3, RTF | 220 pages | ISBN: 9780792376880 | 10.70 Mb

Lattices are geometric objects that can be pictorially described as the set of intersection points of an infinite, regular n-dimensional grid. De spite their apparent simplicity, lattices hide a rich combinatorial struc ture, which has attracted theMoreLattices are geometric objects that can be pictorially described as the set of intersection points of an infinite, regular n-dimensional grid.

De spite their apparent simplicity, lattices hide a rich combinatorial struc ture, which has attracted the attention of great mathematicians over the last two centuries. Not surprisingly, lattices have found numerous ap plications in mathematics and computer science, ranging from number theory and Diophantine approximation, to combinatorial optimization and cryptography. The study of lattices, specifically from a computational point of view, was marked by two major breakthroughs: the development of the LLL lattice reduction algorithm by Lenstra, Lenstra and Lovasz in the early 80s, and Ajtais discovery of a connection between the worst-case and average-case hardness of certain lattice problems in the late 90s.

The LLL algorithm, despite the relatively poor quality of the solution it gives in the worst case, allowed to devise polynomial time solutions to many classical problems in computer science. These include, solving integer programs in a fixed number of variables, factoring polynomials over the rationals, breaking knapsack based cryptosystems, and finding solutions to many other Diophantine and cryptanalysis problems.



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