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Primality testing and integer factorizationh in public-key cryptography

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Contents:

1. Number-theoretic preliminaries
1.1 Problems in number theory
1.2 Groups, rings and fields
1.3 Divisibility properties
1.4 Euclid’s algorithm and continuel fractions
1.5 Arithmetic functions σ (n),τ (n),∅ (n),φ (n),μ (n)
1.6 Linear congruences
1.7 Quadratic congruences
1.8 Primative roots and power residues
1.9 Arithmetic of elliptic curve
1.10 Chapter notes and further reading

2. Primality testing and prime generation
2.1 Computing with numbers and curves
2.2 Riemann and dirichlet L functions
2.3 Rigorous primality tests
2.4 Compositeness and pseudoprimality tests
2.5 Lucas pseudoprimality tests
2.6 Elliptic curve primality tests
2.7 Superpolynomial-time tests
2.8 Polynomial-time tests
2.9 Comparison of general purpose primality tests
2.10 Primality tests for special numbers
2.11 Prime number generation
2.12 Chapter notes and further reading

3. Integer factorization and discrete logarithms
3.1 Introduction
3.2 Simple factoring methods
3.3 Elliptic curve method (ECM)
3.4 General factoring congruence
3.5 Continued FRACtion method (CFRAC)
3.6 Quadratic sieve (QS)
3.7 Number field sieve (NFS)
3.8 Quantum factoring algorithm
3.9 Discrete logarithms
3.10 Kth roots
3.11 Elliptic curve discrete logarithms
3.12 Chapter notes and further reading

4. Number-theoretic cryptography
4.1 Public-key cryptography
4.2 RSA cryptography
4.3 Security and cryptanalysis of RSA
4.4 Rabin cryptography
4.5 Quadratic residuosity cryptography
4.6 Discrete logarithm cryptography
4.7 Elliptic curve cryptography
4.8 Zero-knowledge techniques
4.9 Deniable authentication
4.10 Non-factoring based cryptography
4.11 Chapter notes and further reading

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Availability

Detail Information

Series Title

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Call Number

652.8 YAN P1-2

Publisher

New York : Springer., 2009

Collation

xi, 372 hlm.; ilus.; 25 cm

Language

English

ISBN/ISSN

9780387772677

Classification

652.8

Content Type

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Media Type

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Carrier Type

-

Edition

Second Edition

Subject(s)

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Specific Detail Info

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Statement of Responsibility

Song Y. Yan

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