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An Introduction to Mathematical Cryptography
Jeffrey Hoffstein
Jill Pipher
J.H. Silverman
出版
Springer New York
, 2008-08-12
主題
Mathematics / Number Theory
Computers / Information Theory
Computers / Security / General
Mathematics / Applied
Mathematics / Algebra / Abstract
Mathematics / Probability & Statistics / Stochastic Processes
Language Arts & Disciplines / Library & Information Science / General
Computers / Programming / Algorithms
Computers / Security / Cryptography
Mathematics / Algebra / General
ISBN
0387779930
9780387779935
URL
http://books.google.com.hk/books?id=hqwNDQEACAAJ&hl=&source=gbs_api
註釋
ThecreationofpublickeycryptographybyDi?eandHellmanin1976andthe subsequent invention of the RSA public key cryptosystem by Rivest, Shamir, and Adleman in 1978 are watershed events in the long history of secret c- munications. It is hard to overestimate the importance of public key cr- tosystems and their associated digital signature schemes in the modern world of computers and the Internet. This book provides an introduction to the theory of public key cryptography and to the mathematical ideas underlying that theory. Public key cryptography draws on many areas of mathematics, including number theory, abstract algebra, probability, and information theory. Each of these topics is introduced and developed in su?cient detail so that this book provides a self-contained course for the beginning student. The only prerequisite is a ?rst course in linear algebra. On the other hand, students with stronger mathematical backgrounds can move directly to cryptographic applications and still have time for advanced topics such as elliptic curve pairings and lattice-reduction algorithms. Amongthemanyfacetsofmoderncryptography,thisbookchoosestoc- centrate primarily on public key cryptosystems and digital signature schemes. This allows for an in-depth development of the necessary mathematics - quired for both the construction of these schemes and an analysis of their security. The reader who masters the material in this book will not only be well prepared for further study in cryptography, but will have acquired a real understanding of the underlying mathematical principles on which modern cryptography is based.
