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Primality testing and integer factorization in public-key cryptography

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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)

Computer security
Cryptography

Specific Detail Info

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Statement of Responsibility

Song Y. Yan

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