Complexity of Lattice Problems: A Cryptographic Perspective - download pdf or read online

By Daniele Micciancio,Shafi Goldwasser

Lattices are geometric gadgets that may be pictorially defined because the set of intersection issues of an unlimited, 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 discovered quite a few ap­ plications in arithmetic and machine technology, starting from quantity conception and Diophantine approximation, to combinatorial optimization and cryptography. The examine of lattices, in particular from a computational standpoint, used to be marked through significant breakthroughs: the improvement of the LLL lattice relief 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 definite lattice difficulties within the overdue 90's. The LLL set of rules, regardless of the particularly bad caliber of the answer it supplies within the worst case, allowed to plan polynomial time strategies to many classical difficulties in desktop technological know-how. those comprise, fixing integer courses in a set variety of variables, factoring polynomials over the rationals, breaking knapsack established cryptosystems, and discovering recommendations to many different Diophantine and cryptanalysis problems.

Show description

Read Online or Download Complexity of Lattice Problems: A Cryptographic Perspective (The Springer International Series in Engineering and Computer Science) PDF

Best number theory books

Download e-book for iPad: Number Theory: An Introduction via the Distribution of by Benjamin Fine,Gerhard Rosenberger

This publication presents an advent and assessment of quantity idea in keeping with the distribution and houses of primes. This new angle presents either a company heritage within the ordinary fabric in addition to an summary of the entire self-discipline. all of the crucial themes are lined: basic theorem of mathematics, conception of congruences, quadratic reciprocity, mathematics capabilities, and the distribution of primes.

Get Mathematics of Aperiodic Order (Progress in Mathematics) PDF

What's order that isn't in line with easy repetition, that's, periodicity? How needs to atoms be prepared in a fabric in order that it diffracts like a quasicrystal? How do we describe aperiodically ordered structures mathematically? initially brought on via the – later Nobel prize-winning – discovery of quasicrystals, the research of aperiodic order has given that develop into a well-established and quickly evolving box of mathematical study with shut ties to a stunning number of branches of arithmetic and physics.

Download PDF by Ph. Maennchen: Die Wechselwirkung zwischen Zahlenrechnen und Zahlentheorie

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer ebook records mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen.

Download e-book for kindle: Geometry, Analysis and Probability: In Honor of Jean-Michel by Jean-Benoît Bost,Helmut Hofer,François Labourie,Yves Le

This quantity provides unique examine articles and prolonged surveys on the topic of the mathematical curiosity and paintings of Jean-Michel Bismut. His extraordinary contributions to chance idea and international research on manifolds have had a profound influence on numerous branches of arithmetic within the parts of keep watch over conception, mathematical physics and mathematics geometry.

Additional info for Complexity of Lattice Problems: A Cryptographic Perspective (The Springer International Series in Engineering and Computer Science)

Sample text

Download PDF sample

Complexity of Lattice Problems: A Cryptographic Perspective (The Springer International Series in Engineering and Computer Science) by Daniele Micciancio,Shafi Goldwasser

by Christopher

Rated 4.74 of 5 – based on 48 votes