Complexity of Lattice Problems: A Cryptographic Perspective

Complexity of Lattice Problems: A Cryptographic Perspective (The Springer International Series in Engineering and Computer Science, 671)
- Used Book in Good Condition
Lattices are geometric objects that can be pictorially described as the set of intersection points of an infinite, regular n-dimensional grid. DeÂ spite their apparent simplicity, lattices hide a rich combinatorial strucÂ ture, which has attracted the attention of great mathematicians over the last two centuries. Not surprisingly, lattices have found numerous apÂ 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.
Country USA
Brand Springer
Manufacturer Springer
Binding Hardcover
ItemPartNumber 9780792376880
UnitCount 1
EANs 9780792376880
ReleaseDate 0000-00-00

Country	USA
Brand	Springer
Manufacturer	Springer
Binding	Hardcover
ItemPartNumber	9780792376880
UnitCount	1
EANs	9780792376880
ReleaseDate	0000-00-00

Complexity of Lattice Problems: A Cryptographic Perspective (The Springer International Series in Engineering and Computer Science, 671)

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