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The Development of the Number Field Sieve
The number field sieve is an algorithm for finding the prime factors of large integers. It depends on algebraic number theory. Proposed by John Pollard in 1988, the method was used in 1990 to factor the ninth Fermat number, a 155-digit integer. The algorithm is most suited to numbers of a special form, but there is a promising variant that applies in general. This volume contains six research papers that describe the operation of the number field sieve, from both theoretical and practical perspectives. Pollard's original manuscript is included. In addition, there is an annotated bibliography of directly related literature.
Advances in Cryptology -- CRYPTO 2012
This book constitutes the refereed proceedings of the 32nd Annual International Cryptology Conference, CRYPTO 2012, held in Santa Barbara, CA, USA, in August 2012. The 48 revised full papers presented were carefully reviewed and selected from 225 submissions. The volume also contains the abstracts of two invited talks. The papers are organized in topical sections on symmetric cryptosystems, secure computation, attribute-based and functional encryption, proofs systems, protocols, hash functions, composable security, privacy, leakage and side-channels, signatures, implementation analysis, black-box separation, cryptanalysis, quantum cryptography, and key encapsulation and one-way functions.
Topics in Computational Number Theory Inspired by Peter L. Montgomery
This book highlights the many ideas and algorithms that Peter L. Montgomery has contributed to computational number theory and cryptography.
Guide to Pairing-Based Cryptography
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.
Computational Cryptography
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.
Algorithmic Number Theory
This book constitutes the refereed proceedings of the 4th International Algorithmic Number Theory Symposium, ANTS-IV, held in Leiden, The Netherlands, in July 2000. The book presents 36 contributed papers which have gone through a thorough round of reviewing, selection and revision. Also included are 4 invited survey papers. Among the topics addressed are gcd algorithms, primality, factoring, sieve methods, cryptography, linear algebra, lattices, algebraic number fields, class groups and fields, elliptic curves, polynomials, function fields, and power sums.
The LLL Algorithm
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.
Secret History
The first edition of this award-winning book attracted a wide audience. This second edition is both a joy to read and a useful classroom tool. Unlike traditional textbooks, it requires no mathematical prerequisites and can be read around the mathematics presented. If used as a textbook, the mathematics can be prioritized, with a book both students and instructors will enjoy reading. Secret History: The Story of Cryptology, Second Edition incorporates new material concerning various eras in the long history of cryptology. Much has happened concerning the political aspects of cryptology since the first edition appeared. The still unfolding story is updated here. The first edition of this book ...
Information Security Applications
This book constitutes the refereed proceedings of the 6th International Workshop on Information Security Applications, WISA 2005, held in Jeju Island, Korea, in August 2005. The 29 revised full papers presented were carefully selected during two rounds of reviewing and improvement from 168 submissions. The papers are organized in topical sections on security analysis and attacks, systems security, network security, DRM/software security, efficient HW implementation, side-channel attacks, privacy/anonymity, and efficient implementation.
Topics in Cryptology -- CT-RSA 2006
This book constitutes the refereed proceedings of the Cryptographers' Track at the RSA Conference 2006, CT-RSA 2006, held in San Jose, CA, USA in February 2006. The book presents 24 papers organized in topical sections on attacks on AES, identification, algebra, integrity, public key encryption, signatures, side-channel attacks, CCA encryption, message authentication, block ciphers, and multi-party computation.
