handbook of elliptic and hyperelliptic curve cryptography discrete mathematics and its applications

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Handbook Of Elliptic And Hyperelliptic Curve Cryptography

Author : Henri Cohen
ISBN : 1420034987
Genre : Mathematics
File Size : 20. 41 MB
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The discrete logarithm problem based on elliptic and hyperelliptic curves has gained a lot of popularity as a cryptographic primitive. The main reason is that no subexponential algorithm for computing discrete logarithms on small genus curves is currently available, except in very special cases. Therefore curve-based cryptosystems require much smaller key sizes than RSA to attain the same security level. This makes them particularly attractive for implementations on memory-restricted devices like smart cards and in high-security applications. The Handbook of Elliptic and Hyperelliptic Curve Cryptography introduces the theory and algorithms involved in curve-based cryptography. After a very detailed exposition of the mathematical background, it provides ready-to-implement algorithms for the group operations and computation of pairings. It explores methods for point counting and constructing curves with the complex multiplication method and provides the algorithms in an explicit manner. It also surveys generic methods to compute discrete logarithms and details index calculus methods for hyperelliptic curves. For some special curves the discrete logarithm problem can be transferred to an easier one; the consequences are explained and suggestions for good choices are given. The authors present applications to protocols for discrete-logarithm-based systems (including bilinear structures) and explain the use of elliptic and hyperelliptic curves in factorization and primality proving. Two chapters explore their design and efficient implementations in smart cards. Practical and theoretical aspects of side-channel attacks and countermeasures and a chapter devoted to (pseudo-)random number generation round off the exposition. The broad coverage of all- important areas makes this book a complete handbook of elliptic and hyperelliptic curve cryptography and an invaluable reference to anyone interested in this exciting field.

Selected Areas In Cryptography

Author : Roberto Avanzi
ISBN : 9783642041594
Genre : Computers
File Size : 46. 49 MB
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Selected Areas In Cryptography Sac 2014

Author : Antoine Joux
ISBN : 9783319130514
Genre : Computers
File Size : 33. 71 MB
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This book constitutes the proceedings of the 21st International Conference on Selected Areas in Cryptography, SAC 2014, held in Montreal, QC, Canada, in August 2014. The 22 papers presented in this volume were carefully reviewed and selected from 103 submissions. There are four areas covered at each SAC conference. The three permanent areas are: design and analysis of symmetric key primitives and cryptosystems, including block and stream ciphers, hash function, MAC algorithms, cryptographic permutations, and authenticated encryption schemes; efficient implementations of symmetric and public key algorithms; mathematical and algorithmic aspects of applied cryptology. This year, the fourth area for SAC 2014 is: algorithms for cryptography, cryptanalysis and their complexity analysis.

Pairing Based Cryptography Pairing 2012

Author : Michel Abdalla
ISBN : 9783642363344
Genre : Computers
File Size : 67. 25 MB
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This book constitutes the refereed proceedings of the 5th International Conference on Pairing-Based Cryptography, Pairing 2012, held in Cologne, Germany, in May 2012. The 17 full papers for presentation at the academic track and 3 full papers for presentation at the industrial track were carefully reviewed and selected from 49 submissions. These papers are presented together with 6 invited talks. The contributions are organized in topical sections on: algorithms for pairing computation, security models for encryption, functional encryption, implementations in hardware and software, industry track, properties of pairings, and signature schemes and applications.

Guide To Pairing Based Cryptography

Author : Nadia El Mrabet
ISBN : 9781315353142
Genre : Computers
File Size : 41. 99 MB
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This book is devoted to efficient pairing computations and implementations, useful tools for cryptographers working on topics like identity-based cryptography and the simplification of existing protocols like signature schemes. As well as exploring the basic mathematical background of finite fields and elliptic curves, Guide to Pairing-Based Cryptography offers an overview of the most recent developments in optimizations for pairing implementation. Each chapter includes a presentation of the problem it discusses, the mathematical formulation, a discussion of implementation issues, solutions accompanied by code or pseudocode, several numerical results, and references to further reading and notes. Intended as a self-contained handbook, this book is an invaluable resource for computer scientists, applied mathematicians and security professionals interested in cryptography.

Pearls Of Discrete Mathematics

Author : Martin J. Erickson
ISBN : 1439816166
Genre : Computers
File Size : 61. 75 MB
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This book presents intriguing examples, facts, theorems, and proofs from the world of discrete mathematics. The author presents special topics that are not found elsewhere, including the upward extension of Pascal's triangle, the problem of counting Rook paths and Queen paths, higher-dimensional tic-tac-toe, recurrence relations and generating functions, the pigeonhole principle, information theory and codes, and game theory. He also explores connections between discrete structures and other branches of mathematics, such as combinatorics and algebra. The text includes examples, exercises, and appendices containing Mathematica ® calculations and related Internet resources.

Quantum Communication Measurement And Computing Qcmc

Author : Alexander Lvovsky
ISBN : UCSD:31822037772399
Genre : Computers
File Size : 27. 27 MB
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The volume contains the proceedings of the 2008 International Conference on Quantum Communication, Measurement and Computing. This meeting has been the leading conference in the field for more than two decades. The articles cover quantum information theory, quantum optics, quantum cryptography, experimental tools for quantum information science and related subjects.

Mathematical Reviews

Author :
ISBN : UOM:39015076649873
Genre : Mathematics
File Size : 41. 4 MB
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A Java Library Of Graph Algorithms And Optimization

Author : Hang T. Lau
ISBN : UOM:39076002637754
Genre : Computers
File Size : 75. 80 MB
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Collecting some of the most popular graph algorithms and optimization procedures, A Java Library of Graph Algorithms and Optimization provides the source code for a library of Java programs that can be used to solve problems in graph theory and combinatorial optimization. Self-contained and largely independent, each topic starts with a problem description and an outline of the solution procedure, followed by its parameter list specification, source code, and a test example that illustrates the usage of the code. An accompanying CD-ROM contains all of the Java code included in the book.

Introduction To Combinatorial Designs Second Edition

Author : W.D. Wallis
ISBN : 1584888385
Genre : Mathematics
File Size : 72. 6 MB
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Combinatorial theory is one of the fastest growing areas of modern mathematics. Focusing on a major part of this subject, Introduction to Combinatorial Designs, Second Edition provides a solid foundation in the classical areas of design theory as well as in more contemporary designs based on applications in a variety of fields. After an overview of basic concepts, the text introduces balanced designs and finite geometries. The author then delves into balanced incomplete block designs, covering difference methods, residual and derived designs, and resolvability. Following a chapter on the existence theorem of Bruck, Ryser, and Chowla, the book discusses Latin squares, one-factorizations, triple systems, Hadamard matrices, and Room squares. It concludes with a number of statistical applications of designs. Reflecting recent results in design theory and outlining several applications, this new edition of a standard text presents a comprehensive look at the combinatorial theory of experimental design. Suitable for a one-semester course or for self-study, it will prepare readers for further exploration in the field. To access supplemental materials for this volume, visit the author’s website at http://www.math.siu.edu/Wallis/designs

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