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| 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.
| 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
| 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.
| Author | : Steven D. Galbraith |
| Publisher | : Cambridge University Press |
| Total Pages | : 631 |
| Release | : 2012-03-15 |
| Genre | : Computers |
| ISBN | : 1107013925 |
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 |
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 |
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 |
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 | : Tsuyoshi Takagi |
| Publisher | : Springer Nature |
| Total Pages | : 275 |
| Release | : 2020-10-22 |
| Genre | : Technology & Engineering |
| ISBN | : 981155191X |
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 | : Guochang Xu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 354 |
| Release | : 2007-10-05 |
| Genre | : Science |
| ISBN | : 3540727159 |
This, the second edition of the hugely practical reference and handbook describes kinematic, static and dynamic Global Positioning System theory and applications. It is primarily based upon source-code descriptions of the KSGSoft program developed by the author and his colleagues and used in the AGMASCO project of the EU. This is the first book to report the unified GPS data processing method and algorithm that uses equations for selectively eliminated equivalent observations.
| 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.
