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Primality testing and integer factorization in public-key cryptography

Song Y. Yan - Personal Name;

Table of Contents:

1.Number-Theoretic Preliminaries.-
Problems in Number Theory.
Divisibility Properties.
Euclid's Algorithm and Continued Fractions.
Arithmetic Functions.
Linear Congruences.
Quadratic Congruences.
Primitive Roots and Power Residues.
Arithmetic of Elliptic Curves.
Chapter Notes and Further Reading.-

2.Primality Testing and Prime Generation.-
Computing with Numbers and Curves.
Riemann Zeta and Dirichlet L Functions.
Rigorous Primality Tests.
Compositeness and Pseudoprimality Tests.
Lucas Pseudoprimality Test.
Elliptic Curve Primality Tests.
Superpolynomial-Time Tests.
Polynomial-Time Tests.
Primality Tests for Special Numbers.
Prime Number Generation.
Chapter Notes and Further Reading.-

3.Integer Factorization and Discrete Logarithms.-
Introduction.
Simple Factoring Methods.
Elliptic Curve Method (ECM).
General Factoring Congruence.
Continued FRACtion Method (CFRAC).
Quadratic Sieve (QS).
Number Field Sieve (NFS).
Quantum Factoring Algorithm.
Discrete Logarithms.
kth Roots.
Elliptic Curve Discrete Logarithms.
Chapter Notes and Further Reading.-

4.Number-Theoretic Cryptography.-
Public-Key Cryptography.
RSA Cryptosystem.
Rabin Cryptography.
Quadratic Residuosity Cryptography.
Discrete Logarithm Cryptography.
Elliptic Curve Cryptography.
Zero-Knowledge Techniques.
Deniable Authentication.
Non-Factoring Based Cryptography.
Chapter Notes and Further Reading


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Detail Information
Series Title
Advances in information security ; 11
Call Number
005.8 SON p
Publisher
New York : Springer., 2009
Collation
xviii, 371 hlm.; ilus.: 27 cm.
Language
English
ISBN/ISSN
9780387772677
Classification
005.8
Content Type
-
Media Type
-
Carrier Type
-
Edition
Second Edition
Subject(s)
Cryptography
Computer security
Specific Detail Info
-
Statement of Responsibility
Song Y. Yan
Other version/related

No other version available

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