Complexity of Lattice Problems

Complexity of Lattice Problems
Author: Daniele Micciancio
Publisher: Springer Science & Business Media
Total Pages: 229
Release: 2012-12-06
Genre: Computers
ISBN: 1461508975

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.

A Decade of Lattice Cryptography

A Decade of Lattice Cryptography
Author: Chris Peikert
Publisher:
Total Pages: 156
Release: 2016-03-07
Genre: Computer networks
ISBN: 9781680831122

Surveys most of the major developments in lattice cryptography over the past ten years. The main focus is on the foundational short integer solution (SIS) and learning with errors (LWE) problems, their provable hardness assuming the worst-case intractability of standard lattice problems, and their many cryptographic applications.

The LLL Algorithm

The LLL Algorithm
Author: Phong Q. Nguyen
Publisher: Springer Science & Business Media
Total Pages: 503
Release: 2009-12-02
Genre: Computers
ISBN: 3642022952

The first book to offer a comprehensive view of the LLL algorithm, this text surveys computational aspects of Euclidean lattices and their main applications. It includes many detailed motivations, explanations and examples.

Computational Complexity

Computational Complexity
Author: Sanjeev Arora
Publisher: Cambridge University Press
Total Pages: 609
Release: 2009-04-20
Genre: Computers
ISBN: 0521424267

New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.

Advances in Cryptology – EUROCRYPT 2010

Advances in Cryptology – EUROCRYPT 2010
Author: Henri Gilbert
Publisher: Springer
Total Pages: 706
Release: 2010-05-29
Genre: Computers
ISBN: 3642131905

These are the proceedings of Eurocrypt 2010, the 29th in the series of Eu- pean conferences on the Theory and Application of Cryptographic Techniques. The conference was sponsored by the International Association for Cryptologic Research and held on the French Riviera, May 30–June 3, 2010. A total of 191 papers were received of which 188 were retained as valid submissions. These were each assigned to at least three Program Committee members and a total of 606 review reports were produced. The printed record of the reviews and extensive online discussions that followed would be almost as voluminous as these proceedings. In the end 35 submissions were accepted with twosubmissionpairsbeingmergedtogive33paperspresentedattheconference. The ?nal papers in these proceedings were not subject to a second review before publication and the authors are responsible for their contents. The ProgramCommittee, listed on the next page, deservesparticular thanks for all their hard work, their outstanding expertise, and their constant c- mitment to all aspects of the evaluation process. These thanks are of course extended to the very many external reviewers who took the time to help out during the evaluation process.It was also a greatpleasure to honor and welcome Moti Yung who gave the 2010 IACR Distinguished Lecture.

Lattice Basis Reduction

Lattice Basis Reduction
Author: Murray R. Bremner
Publisher: CRC Press
Total Pages: 330
Release: 2011-08-12
Genre: Computers
ISBN: 1439807043

First developed in the early 1980s by Lenstra, Lenstra, and Lovasz, the LLL algorithm was originally used to provide a polynomial-time algorithm for factoring polynomials with rational coefficients. It very quickly became an essential tool in integer linear programming problems and was later adapted for use in cryptanalysis. This book provides an i

Advances in Cryptology - CRYPTO 2007

Advances in Cryptology - CRYPTO 2007
Author: Alfred Menezes
Publisher: Springer
Total Pages: 643
Release: 2007-08-10
Genre: Computers
ISBN: 3540741437

This volume constitutes the refereed proceedings of the 27th Annual International Cryptology Conference held in Santa Barbara, California, in August 2007. Thirty-three full papers are presented along with one important invited lecture. The papers address current foundational, theoretical, and research aspects of cryptology, cryptography, and cryptanalysis. In addition, readers will discover many advanced and emerging applications.

Complexity of Infinite-Domain Constraint Satisfaction

Complexity of Infinite-Domain Constraint Satisfaction
Author: Manuel Bodirsky
Publisher: Cambridge University Press
Total Pages: 537
Release: 2021-06-10
Genre: Computers
ISBN: 1107042844

Introduces the universal-algebraic approach to classifying the computational complexity of constraint satisfaction problems.

Lattice Coding for Signals and Networks

Lattice Coding for Signals and Networks
Author: Ram Zamir
Publisher: Cambridge University Press
Total Pages: 459
Release: 2014-08-07
Genre: Technology & Engineering
ISBN: 1139991590

Unifying information theory and digital communication through the language of lattice codes, this book provides a detailed overview for students, researchers and industry practitioners. It covers classical work by leading researchers in the field of lattice codes and complementary work on dithered quantization and infinite constellations, and then introduces the more recent results on 'algebraic binning' for side-information problems, and linear/lattice codes for networks. It shows how high dimensional lattice codes can close the gap to the optimal information theoretic solution, including the characterisation of error exponents. The solutions presented are based on lattice codes, and are therefore close to practical implementations, with many advanced setups and techniques, such as shaping, entropy-coding, side-information and multi-terminal systems. Moreover, some of the network setups shown demonstrate how lattice codes are potentially more efficient than traditional random-coding solutions, for instance when generalising the framework to Gaussian networks.

Coding and Cryptology

Coding and Cryptology
Author: Yeow Meng Chee
Publisher: Springer
Total Pages: 302
Release: 2011-06-05
Genre: Computers
ISBN: 3642209017

This book constitutes the refereed proceedings of the Third International Workshop on Coding and Cryptology, IWCC 2011, held in Qingdao, China, May 30-June 3, 2011. The 19 revised full technical papers are contributed by the invited speakers of the workshop. The papers were carefully reviewed and cover a broad range of foundational and methodological as well as applicative issues in coding and cryptology, as well as related areas such as combinatorics.