Lattice Basis Reduction
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Lattice Basis Reduction
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Author : Murray R. Bremner
language : en
Publisher: CRC Press
Release Date : 2011-08-12
Lattice Basis Reduction written by Murray R. Bremner and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-12 with Computers categories.
First developed in the early 1980s by Lenstra, Lenstra, and Lovász, 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 introduction to the theory and applications of lattice basis reduction and the LLL algorithm. With numerous examples and suggested exercises, the text discusses various applications of lattice basis reduction to cryptography, number theory, polynomial factorization, and matrix canonical forms.
Mathematics Of Public Key Cryptography
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Author : Steven D. Galbraith
language : en
Publisher: Cambridge University Press
Release Date : 2012-03-15
Mathematics Of Public Key Cryptography written by Steven D. Galbraith and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-15 with Computers categories.
This advanced graduate textbook gives an authoritative and insightful description of the major ideas and techniques of public key cryptography.
Lattice Basis Reduction
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Author : Murray R. Bremner
language : en
Publisher: CRC Press
Release Date : 2011-08-12
Lattice Basis Reduction written by Murray R. Bremner and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-12 with Computers categories.
First developed in the early 1980s by Lenstra, Lenstra, and Lovász, 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 introduction to the theory and applications of lattice basis reduction and the LLL algorithm. With numerous examples and suggested exercises, the text discusses various applications of lattice basis reduction to cryptography, number theory, polynomial factorization, and matrix canonical forms.
The Lll Algorithm
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Author : Phong Q. Nguyen
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-02
The Lll Algorithm written by Phong Q. Nguyen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-02 with Computers categories.
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.
Complexity Of Lattice Problems
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Author : Daniele Micciancio
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Complexity Of Lattice Problems written by Daniele Micciancio and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
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.
Lattice Basis Reduction Algorithms And Their Applications
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Author : Gudrun Susanne Wetzel
language : en
Publisher:
Release Date : 1998
Lattice Basis Reduction Algorithms And Their Applications written by Gudrun Susanne Wetzel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
Cryptanalysis Of Rsa And Its Variants
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Author : M. Jason Hinek
language : en
Publisher: CRC Press
Release Date : 2009-07-21
Cryptanalysis Of Rsa And Its Variants written by M. Jason Hinek and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-21 with Computers categories.
Thirty years after RSA was first publicized, it remains an active research area. Although several good surveys exist, they are either slightly outdated or only focus on one type of attack. Offering an updated look at this field, Cryptanalysis of RSA and Its Variants presents the best known mathematical attacks on RSA and its main variants, includin
Cryptology And Computational Number Theory
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Author : Carl Pomerance
language : en
Publisher: American Mathematical Soc.
Release Date : 1990
Cryptology And Computational Number Theory written by Carl Pomerance and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Computers categories.
In the past dozen or so years, cryptology and computational number theory have become increasingly intertwined. Because the primary cryptologic application of number theory is the apparent intractability of certain computations, these two fields could part in the future and again go their separate ways. But for now, their union is continuing to bring ferment and rapid change in both subjects. This book contains the proceedings of an AMS Short Course in Cryptology and Computational Number Theory, held in August 1989 during the Joint Mathematics Meetings in Boulder, Colorado. These eight papers by six of the top experts in the field will provide readers with a thorough introduction to some of the principal advances in cryptology and computational number theory over the past fifteen years. In addition to an extensive introductory article, the book contains articles on primality testing, discrete logarithms, integer factoring, knapsack cryptosystems, pseudorandom number generators, the theoretical underpinnings of cryptology, and other number theory-based cryptosystems. Requiring only background in elementary number theory, this book is aimed at nonexperts, including graduate students and advanced undergraduates in mathematics and computer science.
A Decade Of Lattice Cryptography
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Author : Chris Peikert
language : en
Publisher:
Release Date : 2016-03-07
A Decade Of Lattice Cryptography written by Chris Peikert and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-07 with Computer networks categories.
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.
Application Of Lattice Basis Reduction
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Author : Lena Likavec
language : en
Publisher:
Release Date : 2011
Application Of Lattice Basis Reduction written by Lena Likavec and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.