The Springer International Series in Engineering and Computer Science

Complexity of Lattice Problems

A Cryptographic Perspective

Authors: Micciancio, Daniele, Goldwasser, Shafi

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About this book

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.

Table of contents (9 chapters)

Buy this book

eBook $89.00
price for USA (gross)
  • ISBN 978-1-4615-0897-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $239.00
price for USA
  • ISBN 978-0-7923-7688-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • ISBN 978-1-4613-5293-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Complexity of Lattice Problems
Book Subtitle
A Cryptographic Perspective
Authors
Series Title
The Springer International Series in Engineering and Computer Science
Series Volume
671
Copyright
2002
Publisher
Springer US
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4615-0897-7
DOI
10.1007/978-1-4615-0897-7
Hardcover ISBN
978-0-7923-7688-0
Softcover ISBN
978-1-4613-5293-8
Series ISSN
0893-3405
Edition Number
1
Number of Pages
X, 220
Topics