Download Complexity of Lattice Problems: A Cryptographic Perspective by Daniele Micciancio,Shafi Goldwasser PDF

By Daniele Micciancio,Shafi Goldwasser

Lattices are geometric gadgets that may be pictorially defined because the set of intersection issues of an unlimited, common n-dimensional grid. De­ spite their obvious simplicity, lattices disguise a wealthy combinatorial struc­ ture, which has attracted the eye of serious mathematicians over the past centuries. now not unusually, lattices have came upon a variety of ap­ plications in arithmetic and machine technological know-how, starting from quantity concept and Diophantine approximation, to combinatorial optimization and cryptography. The examine of lattices, in particular from a computational standpoint, used to be marked by way of significant breakthroughs: the improvement of the LLL lattice aid set of rules via Lenstra, Lenstra and Lovasz within the early 80's, and Ajtai's discovery of a connection among the worst-case and average-case hardness of yes lattice difficulties within the past due 90's. The LLL set of rules, regardless of the rather terrible caliber of the answer it offers within the worst case, allowed to plan polynomial time ideas to many classical difficulties in computing device technological know-how. those comprise, fixing integer courses in a hard and fast variety of variables, factoring polynomials over the rationals, breaking knapsack dependent cryptosystems, and discovering options to many different Diophantine and cryptanalysis problems.

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