An Introduction to Mathematical Cryptography
Jeffrey Hoffstein, Jill Pipher, Joseph H. Silverman
SpringerVerlag – Undergraduate Texts in Mathematics
ISBN: 9781493917105
– 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 graduatelevel text that provides a
selfcontained 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 DiffieHellmann key
exchange, discrete logarithmbased 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 indepth treatment of important recent cryptographic innovations,
such as elliptic curves, elliptic curve and pairingbased
cryptography, lattices, latticebased cryptography, and the NTRU
cryptosystem.
Additional topics, including hash functions, pseudorandom number
generators, zeroknowledge 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 DiffieHellman
 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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