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Mathematics - Number Theory and Discrete Mathematics | An Introduction to Mathematical Cryptography

An Introduction to Mathematical Cryptography

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

Softcover reprint of hardcover 1st ed. 2008

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  • Detailed introduction to elliptic curves and how they're used in cryptography, including the "hot" recent topic of elliptic curve pairing-based cryptography
  • Detailed introduction to lattices and lattice based cryptography
  • Provides an entry for graduate students into an active field of research
  • Includes exercises and examples at the end of each section
  • A standard reference for researchers in the field
  • May be implemented in a classroom setting or independent study

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.

Content Level » Graduate

Keywords » AES - Crib - DES - Number theory - algorithms - cryptography - cryptology - information - information theory

Related subjects » Algebra - Applications - Number Theory and Discrete Mathematics - Security and Cryptology - Theoretical Computer Science

Table of 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.

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