The Lll Algorithm
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Author | : Phong Q. Nguyen |
Publisher | : Springer Science & Business Media |
Total Pages | : 503 |
Release | : 2009-12-02 |
Genre | : Computers |
ISBN | : 3642022952 |
Download The LLL Algorithm Book in PDF, Epub and Kindle
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.
Author | : Murray R. Bremner |
Publisher | : CRC Press |
Total Pages | : 330 |
Release | : 2011-08-12 |
Genre | : Computers |
ISBN | : 1439807043 |
Download Lattice Basis Reduction Book in PDF, Epub and Kindle
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
Author | : Daniele Micciancio |
Publisher | : Springer Science & Business Media |
Total Pages | : 229 |
Release | : 2012-12-06 |
Genre | : Computers |
ISBN | : 1461508975 |
Download Complexity of Lattice Problems Book in PDF, Epub and Kindle
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.
Author | : Steven D. Galbraith |
Publisher | : Cambridge University Press |
Total Pages | : 631 |
Release | : 2012-03-15 |
Genre | : Computers |
ISBN | : 1107013925 |
Download Mathematics of Public Key Cryptography Book in PDF, Epub and Kindle
This advanced graduate textbook gives an authoritative and insightful description of the major ideas and techniques of public key cryptography.
Author | : Henri Cohen |
Publisher | : Springer Science & Business Media |
Total Pages | : 556 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 3662029456 |
Download A Course in Computational Algebraic Number Theory Book in PDF, Epub and Kindle
A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods, including a detailed description of the number field sieve algorithm. The whole is rounded off with a description of available computer packages and some useful tables, backed by numerous exercises. Written by an authority in the field, and one with great practical and teaching experience, this is certain to become the standard and indispensable reference on the subject.
Author | : Joppe Bos |
Publisher | : |
Total Pages | : 402 |
Release | : 2021-12-09 |
Genre | : Language Arts & Disciplines |
ISBN | : 1108848427 |
Download Computational Cryptography Book in PDF, Epub and Kindle
The area of computational cryptography is dedicated to the development of effective methods in algorithmic number theory that improve implementation of cryptosystems or further their cryptanalysis. This book is a tribute to Arjen K. Lenstra, one of the key contributors to the field, on the occasion of his 65th birthday, covering his best-known scientific achievements in the field. Students and security engineers will appreciate this no-nonsense introduction to the hard mathematical problems used in cryptography and on which cybersecurity is built, as well as the overview of recent advances on how to solve these problems from both theoretical and practical applied perspectives. Beginning with polynomials, the book moves on to the celebrated Lenstra-Lenstra-Lovász lattice reduction algorithm, and then progresses to integer factorization and the impact of these methods to the selection of strong cryptographic keys for usage in widely used standards.
Author | : Charles C. Sims |
Publisher | : Cambridge University Press |
Total Pages | : 624 |
Release | : 1994-01-28 |
Genre | : Mathematics |
ISBN | : 0521432138 |
Download Computation with Finitely Presented Groups Book in PDF, Epub and Kindle
Research in computational group theory, an active subfield of computational algebra, has emphasised three areas: finite permutation groups, finite solvable groups, and finitely presented groups. This book deals with the third of these areas. The author emphasises the connections with fundamental algorithms from theoretical computer science, particularly the theory of automata and formal languages, computational number theory, and computational commutative algebra. The LLL lattice reduction algorithm and various algorithms for Hermite and Smith normal forms from computational number theory are used to study the abelian quotients of a finitely presented group. The work of Baumslag, Cannonito and Miller on computing nonabelian polycyclic quotients is described as a generalisation of Buchberger's Gröbner basis methods to right ideals in the integral group ring of a polycyclic group. Researchers in computational group theory, mathematicians interested in finitely presented groups and theoretical computer scientists will find this book useful.
Author | : Nigel P. Smart |
Publisher | : Cambridge University Press |
Total Pages | : 264 |
Release | : 1998-11-12 |
Genre | : Mathematics |
ISBN | : 9780521646338 |
Download The Algorithmic Resolution of Diophantine Equations Book in PDF, Epub and Kindle
A coherent account of the computational methods used to solve diophantine equations.
Author | : Tsuyoshi Takagi |
Publisher | : Springer Nature |
Total Pages | : 275 |
Release | : 2020-10-22 |
Genre | : Technology & Engineering |
ISBN | : 981155191X |
Download International Symposium on Mathematics, Quantum Theory, and Cryptography Book in PDF, Epub and Kindle
This open access book presents selected papers from International Symposium on Mathematics, Quantum Theory, and Cryptography (MQC), which was held on September 25-27, 2019 in Fukuoka, Japan. The international symposium MQC addresses the mathematics and quantum theory underlying secure modeling of the post quantum cryptography including e.g. mathematical study of the light-matter interaction models as well as quantum computing. The security of the most widely used RSA cryptosystem is based on the difficulty of factoring large integers. However, in 1994 Shor proposed a quantum polynomial time algorithm for factoring integers, and the RSA cryptosystem is no longer secure in the quantum computing model. This vulnerability has prompted research into post-quantum cryptography using alternative mathematical problems that are secure in the era of quantum computers. In this regard, the National Institute of Standards and Technology (NIST) began to standardize post-quantum cryptography in 2016. This book is suitable for postgraduate students in mathematics and computer science, as well as for experts in industry working on post-quantum cryptography.
Author | : Xiaoyun Wang |
Publisher | : CRC Press |
Total Pages | : 228 |
Release | : 2015-10-22 |
Genre | : Computers |
ISBN | : 1498702244 |
Download Mathematical Foundations of Public Key Cryptography Book in PDF, Epub and Kindle
In Mathematical Foundations of Public Key Cryptography, the authors integrate the results of more than 20 years of research and teaching experience to help students bridge the gap between math theory and crypto practice. The book provides a theoretical structure of fundamental number theory and algebra knowledge supporting public-key cryptography.R