An Introduction to Mathematical Cryptography
Jeffrey Hoffstein, Jill Pipher, Joseph H. Silverman
Springer-Verlag – Undergraduate Texts in Mathematics
ISBN: 978-1-4939-1710-5
– 2nd ed.
– © 2014
– 538 + xv pages
Math. Subj. Class: Primary 94A60; Secondary 11T71, 14G50
Available from
Amazon
and direct from
Springer.
An Introduction to Mathematical Cryptography is an advanced
undergraduate/beginning graduate-level text that provides a
self-contained introduction to modern cryptography, with an emphasis on 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.
Additional topics, including hash functions, pseudorandom number
generators, zero-knowledge proofs, quantum computation, and DES/AES,
are briefly described in the final chapter. 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.
Contents
- An Introduction to Cryptography
- Discrete Logarithms and Diffie-Hellman
- Integer Factorization and RSA
- Probability Theory and Information Theory
- Elliptic Curves and Cryptography
- Lattices and Cryptography
- Digital Signatures
- Additional Topics in Cryptology
No book is ever free from error or incapable of being improved. We
would be delighted to receive comments, positive or negative, and corrections
from our readers. You can send mail to us at
mathcrypto@math.brown.edu
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