An Introduction to Mathematical Cryptography
Springer-Verlag New York Inc.
978-1-4939-3938-1 (ISBN)
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.
Dr. Jeffrey Hoffstein has been a professor at Brown University since 1989 and has been a visiting professor and tenured professor at several other universities since 1978. His research areas are number theory, automorphic forms and cryptography. He has authored more than 50 publications. Dr. Jill Pipher has been a professor at Brown University since 1989. She has been an invited lecturer and has received numerous awards and honors. Her research areas are harmonic analysis, elliptic PDE, and cryptography. She has authored over 40 publications. Dr. Joseph Silverman has been a professor at Brown University since 1988. He served as the Chair of the Brown Mathematics department from 2001–2004. He has received numerous fellowships, grants and awards and is a frequently invited lecturer. His research areas are number theory, arithmetic geometry, elliptic curves, dynamical systems and cryptography. He has authored more than 130 publications and has had more than 20 doctoral students.
Preface.- Introduction.- 1 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.- List of Notation.- References.- Index.
| Erscheinungsdatum | 22.09.2016 |
|---|---|
| Reihe/Serie | Undergraduate Texts in Mathematics |
| Zusatzinfo | 32 Illustrations, black and white; XVII, 538 p. 32 illus. |
| Verlagsort | New York |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Informatik ► Theorie / Studium ► Algorithmen |
| Informatik ► Theorie / Studium ► Kryptologie | |
| Mathematik / Informatik ► Mathematik ► Algebra | |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie | |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| Schlagworte | coding theory • Digital Signatures • discrete logarithms • Elliptic Curves • Information Theory • lattices and cryptography • Probability Theory |
| ISBN-10 | 1-4939-3938-6 / 1493939386 |
| ISBN-13 | 978-1-4939-3938-1 / 9781493939381 |
| Zustand | Neuware |
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