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. This text provides 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.
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 cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem.
The second edition of __An Introduction to Mathematical Cryptography__ includes a significant revision of the material on digital signatures, including an earlier introduction to RSA, Elgamal, and DSA signatures, and new material on lattice-based signatures and rejection sampling. Many sections have been rewritten or expanded for clarity, especially in the chapters on information theory, elliptic curves, and lattices, and the chapter of additional topics has been expanded to include sections on digital cash and homomorphic encryption. Numerous new exercises have been included.

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Jeffrey Hoffstein; Jill Catherine Pipher; Joseph H Silverman

Hoffstein, Jeffrey, Pipher, Jill, Silverman, Joseph H.

Adobe InDesign CS6 (Windows)

Springer New York : Imprint : Springer

Springer US

Springer Nature (Textbooks & Major Reference Works), [New York], 2010

Undergraduate texts in mathematics, 2nd ed. 2014, New York, NY, 2014

Undergraduate texts in mathematics, Second edition, New York, 2014

United States, United States of America

Sep 11, 2014

sm40010754

producers:
Adobe PDF Library 10.0.1; modified using iText® 5.3.1 ©2000-2012 1T3XT BVBA (AGPL-version)

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Source title: An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics)

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. This text provides 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.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, anddigital signatures;fundamental mathematical tools for cryptography, including primality testing, factorization algorithms, probability theory, information theory, and collision algorithms;an in-depth treatment of important cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem.The second edition of An Introduction to Mathematical Cryptography includes a significant revision of the material on digital signatures, including an earlier introduction to RSA, Elgamal, and DSA signatures, and new material on lattice-based signatures and rejection sampling. Many sections have been rewritten or expanded for clarity, especially in the chapters on information theory, elliptic curves, and lattices, and the chapter of additional topics has been expanded to include sections on digital cash and homomorphic encryption. Numerous new exercises have been included.
Erscheinungsdatum: 11.09.2014

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. This text provides 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.
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 cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem.
The second edition of An Introduction to Mathematical Cryptography includes a significant revision of the material on digital signatures, including an earlier introduction to RSA, Elgamal, and DSA signatures, and new material on lattice-based signatures and rejection sampling. Many sections have been rewritten or expanded for clarity, especially in the chapters on information theory, elliptic curves, and lattices, and the chapter of additional topics has been expanded to include sections on digital cash and homomorphic encryption. Numerous new exercises have been included.

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.

Front Matter....Pages i-xvii
An Introduction to Cryptography....Pages 1-59
Discrete Logarithms and Diffie–Hellman....Pages 61-115
Integer Factorization and RSA....Pages 117-191
Digital Signatures....Pages 193-205
Combinatorics, Probability, and Information Theory....Pages 207-298
Elliptic Curves and Cryptography....Pages 299-371
Lattices and Cryptography....Pages 373-470
Additional Topics in Cryptography....Pages 471-501
Back Matter....Pages 503-538

An Introduction To Cryptography -- 2 Discrete Logarithms And Diffie-hellman -- 3 Integer Factorization And Rsa -- 4 Digital Signatures -- 5 Combinatorics, Probability, And Information Theory -- 6 Elliptic Curves And Cryptography -- 7 Lattices And Cryptography -- 8 Additional Topics In Cryptography. Jeffrey Hoffstein, Jill Pipher, Joseph H. Silverman. Includes Bibliographical References And Index.

2014-11-10