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Author: Phong Q. Nguyen
Publisher: Springer Science & Business Media
ISBN: 3642022952
Category : Computers
Languages : en
Pages : 503
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Book Description
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: Phong Q. Nguyen
Publisher: Springer Science & Business Media
ISBN: 3642022952
Category : Computers
Languages : en
Pages : 503
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Book Description
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
ISBN: 1439807043
Category : Computers
Languages : en
Pages : 330
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Book Description
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: Jeremy Avigad
Publisher: Springer
ISBN: 3319948210
Category : Mathematics
Languages : en
Pages : 657
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Book Description
This book constitutes the refereed proceedings of the 9th International Conference on Interactive Theorem Proving, ITP 2018, held in Oxford, UK, in July 2018. The 32 full papers and 5 short papers presented were carefully reviewed and selected from 65 submissions. The papers feature research in the area of logical frameworks and interactive proof assistants. The topics include theoretical foundations and implementation aspects of the technology, as well as applications to verifying hardware and software systems to ensure their safety and security, and applications to the formal verication of mathematical results. Chapters 2, 10, 26, 29, 30 and 37 are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
Author: Daniele Micciancio
Publisher: Springer Science & Business Media
ISBN: 1461508975
Category : Computers
Languages : en
Pages : 229
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Book Description
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
ISBN: 1107013925
Category : Computers
Languages : en
Pages : 631
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Book Description
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
ISBN: 3662029456
Category : Mathematics
Languages : en
Pages : 556
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Book Description
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: Steven D. Galbraith
Publisher: Springer Nature
ISBN: 3030346218
Category : Computers
Languages : en
Pages : 675
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Book Description
The three-volume set of LNCS 11921,11922, and 11923 constitutes the refereed proceedings of the 25th International Conference on the Theory and Applications of Cryptology and Information Security, ASIACRYPT 2019, held in Kobe, Japan, in December 2019. The 71 revised full papers presented were carefully reviewed and selected from 307 submissions. They are organized in topical sections on Lattices; Symmetric Cryptography; Isogenies; Obfuscation; Multiparty Computation; Quantum; E-cash and Blockchain; Codes; Authenticated Encryption; Multilinear Maps; Homomorphic Encryption; Combinatorial Cryptography; Signatures; Public Key Encryption; Side Channels; Functional Encryption; Zero Knowledge.
Author: Joppe Bos
Publisher: Cambridge University Press
ISBN: 1108795935
Category : Language Arts & Disciplines
Languages : en
Pages : 400
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Book Description
A guide to cryptanalysis and the implementation of cryptosystems, written for students and security engineers by leading experts.
Author: Charles C. Sims
Publisher: Cambridge University Press
ISBN: 0521432138
Category : Mathematics
Languages : en
Pages : 624
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Book Description
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: Kwok Y. Lam
Publisher: Birkhäuser
ISBN: 3034882955
Category : Computers
Languages : en
Pages : 376
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Book Description
This volume contains the refereed proceedings of the Workshop on Cryptography and Computational Number Theory, CCNT'99, which has been held in Singapore during the week of November 22-26, 1999. The workshop was organized by the Centre for Systems Security of the Na tional University of Singapore. We gratefully acknowledge the financial support from the Singapore National Science and Technology Board under the grant num ber RP960668/M. The idea for this workshop grew out of the recognition of the recent, rapid development in various areas of cryptography and computational number the ory. The event followed the concept of the research programs at such well-known research institutions as the Newton Institute (UK), Oberwolfach and Dagstuhl (Germany), and Luminy (France). Accordingly, there were only invited lectures at the workshop with plenty of time for informal discussions. It was hoped and successfully achieved that the meeting would encourage and stimulate further research in information and computer security as well as in the design and implementation of number theoretic cryptosystems and other related areas. Another goal of the meeting was to stimulate collaboration and more active interaction between mathematicians, computer scientists, practical cryptographers and engineers in academia, industry and government.
