By Daniele Micciancio
Lattices are geometric items that may be pictorially defined because the set of intersection issues of an enormous, standard n-dimensional grid. De spite their obvious simplicity, lattices cover a wealthy combinatorial struc ture, which has attracted the eye of serious mathematicians over the past centuries. no longer strangely, lattices have came upon quite a few 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, was once marked via significant breakthroughs: the improvement of the LLL lattice aid set of rules by way of 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 sure lattice difficulties within the overdue 90's. The LLL set of rules, regardless of the quite terrible caliber of the answer it provides within the worst case, allowed to plan polynomial time options to many classical difficulties in desktop technology. those comprise, fixing integer courses in a hard and fast variety of variables, factoring polynomials over the rationals, breaking knapsack dependent cryptosystems, and discovering strategies to many different Diophantine and cryptanalysis difficulties.
Read Online or Download Complexity of Lattice Problems: A Cryptographic Perspective (The Springer International Series in Engineering and Computer Science) PDF
Similar Information Theory books
Spectral thought of Random Matrices
Community coding is a box of data and coding concept and is a technique of achieving greatest details move in a community. This booklet is a perfect creation for the communications and community engineer, operating in learn and improvement, who wishes an intuitive creation to community coding and to the elevated functionality and reliability it deals in lots of purposes.
A brand new self-discipline, Quantum info technological know-how, has emerged within the final twenty years of the 20th century on the intersection of Physics, arithmetic, and computing device technological know-how. Quantum details Processing is an program of Quantum info technological know-how which covers the transformation, garage, and transmission of quantum details; it represents a progressive method of info processing.
Extra info for Complexity of Lattice Problems: A Cryptographic Perspective (The Springer International Series in Engineering and Computer Science)