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An Introduction to Mathematical Cryptography

Author: J H Silverman; Jill Pipher; Jeffrey Hoffstein
Publisher: New York, NY : Springer New York, 2008.
Series: Undergraduate texts in mathematics
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and  Read more...
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Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: J H Silverman; Jill Pipher; Jeffrey Hoffstein
ISBN: 0387779949 9780387779942 661195421X 9786611954215
OCLC Number: 1066469683
Description: 1 online resource (XVI, 524 pages 29 illustrations) : online resource
Contents: An Introduction to Cryptography --
Discrete Logarithms and Diffie Hellman --
Integer Factorization and RSA --
Combinatorics, Probability and Information Theory --
Elliptic Curves and Cryptography --
Lattices and Cryptography --
Digital Signatures --
Additional Topics in Cryptography.
Series Title: Undergraduate texts in mathematics
Responsibility: by J.H. Silverman, Jill Pipher, Jeffrey Hoffstein.

Abstract:

This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include: * classical cryptographic constructions, such as Diffie-Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, and digital signatures; * fundamental mathematical tools for cryptography, including primality testing, factorization algorithms, probability theory, information theory, and collision algorithms; * an in-depth treatment of important recent cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem. This book is an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online.

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