Complexity of Lattice Problems: A Cryptographic Perspective: 671 - Brossura

Micciancio, Daniele; Goldwasser, Shafi

Brossura

ISBN 10: 1461352932 ISBN 13: 9781461352938

Casa editrice: Springer, 2012

Riassunto

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 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 80's, and Ajtai's discovery of a connection between the worst-case and average-case hardness of certain lattice problems in the late 90's. 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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Contenuti

Preface. 1. Basics. 2. Approximation Algorithms. 3. Closest Vector Problem. 4. Shortest Vector Problem. 5. Sphere Packings. 6. Low-Degree Hypergraphs. 7. Basis Reduction Problems. 8. Cryptographic Functions. 9. Interactive Proof Systems. Index

Dettagli dell?edizione

• Editore: Springer
• Data di pubblicazione: 2012
• ISBN 10: 1461352932
• ISBN 13: 9781461352938
• Rilegatura: Copertina flessibile
• Lingua: Inglese
• Numero di pagine: 236