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Cryptography of number theoretic ciphers

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Termasuk bibliografi dan indeks.

CONTENTS:

Terminology of Cryptography

Notation

Types of Attacks

Public Key Ciphers

Block and Stream Ciphers

Protocols



Probability Theory

Definitions

The Birthday Problem

Random Variables



Divisibility and Arithmetic

Divisibility

Arithmetic with Large Integers

Greatest Common Divisors and the Euclidean Algorithm



Primes

The Fundamental Theorem of Arithmetic

The Distribution of Prime Numbers

Identifying and Finding Primes

The Largest Prime Factor of a Number



Congruences

Simple Properties of Congruences

Linear Congruences

The Chinese Remainder Theorem



Euler's Theorem and Its Consequences

Fermat's Little Theorem

Euler's Theorem

Primitive Roots

Discrete Logarithms



Second Degree Congruences

The Legendre Symbol

The Law of Quadratic Reciprocity

The Jacobi Symbol

Euler Pseudoprimes

Solving Quadratic Congruences Modulo m



Information Theory

Entropy

Perfect Secrecy

Unicity Distance

Some Obsolete Ciphers

The Entropy of Number Theoretic Ciphers



Groups, Rings and Fields

Groups

Simple Properties of Groups

The Baby-Step-Giant-Step Algorithm

Rings and Fields

Polynomials

Algebraic Number Theory



Exponential Methods of Factoring Integers

Fermat's Difference of Squares Method

Pollard's Rho Method

Pollard's p - 1 Method

Square Form Factorization



Finding Large Primes

Stronger Probable Prime Tests

Lucas Probable Prime Tests

Rigorous Proof of Primality

Prime Proofs for Arbitrary Large Integers



Elliptic Curves

Definitions and Examples

Factoring with Elliptic Curves

Primality Proving with Elliptic Curves



Subexponential Factoring Algorithms

Factoring with Continued Fractions

The Quadratic Sieve

Variations of the Quadratic Sieve

Large Primes

Multiple Polynomials

The Self-Initializing Quadratic Sieve

The Number Field Sieve



Computing Discrete Logarithms

Shanks' Baby-Step-Giant-Step Method

Pollard's Methods

The Rho Method for Discrete Logarithms

The Lambda Method for Discrete Logarithms

Discrete Logarithms via Index Calculus

Other Fast Methods for the Group R[subscript m]



Random Number Generation

Linear Feedback Shift Registers

A Quadratic Residue Random Number Generator

Hash Functions

Generating Truly Random Numbers



The Cryptographic Algorithms

Private Key Ciphers

Rijndael, the Advanced Encryption Standard

Byte Arithmetic in Rijndael

Word Arithmetic in Rijndael

The Structure of Rijndael

The Key Schedule of Rijndael

Summary of Rijndael

The Pohlig-Hellman Cipher

Elliptic Curve Pohlig-Hellman



Public Key Ciphers

Rivest-Shamir-Adleman

Massey-Omura

Elliptic Curve Massey-Omura

ElGamal

Elliptic Curve ElGamal

Rabin-Williams

Exercises

Signature Algorithms

Rivest-Shamir-Adleman Signatures

ElGamal Signatures

Rabin-Williams Signatures

The Digital Signature Algorithm



Key Exchange Algorithms

Key Exchange Using a Trusted Server

The Diffie-Hellman Key Exchange

The X.509 Key Exchange



Simple Protocols

Bit Commitment

Mental Poker

Oblivious Transfer

Zero-knowledge Proofs

Methods of Sharing Secrets

Secret Splitting

The Lagrange Interpolating Polynomial Scheme

The Asmuth and Bloom Threshold Scheme

Blind Signatures


Complicated Protocols

Contract Signing

Secure Elections

Electronic Cash

Electronic Cash According to Chaum

Electronic Cash According to Brands



Complete Systems

Kerberos

Pretty Good Privacy



Methods of Attack

Direct Attacks

Try All Keys

Factor a Large Integer

Solve a Discrete Logarithm Problem

Timing Attacks



Exploiting an Error

Key Management

Reuse of a Key

Bad Parameter Choice

Partial Key Exposure

Computer Failure



Active Attacks

Force a User to Make a Mistake

Man-in-the-Middle Attacks

Birthday Attacks

Subliminal Channels

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Availability

Detail Information

Series Title

Computational mathematics series

Call Number

005.8 WAG c

Publisher

Florida : Chapman & Hall/CRC., 2002

Collation

xv, 318 hlm.; ilus.; 24 cm.

Language

English

ISBN/ISSN

1584881534

Classification

005.8

Content Type

-

Media Type

-

Carrier Type

-

Edition

null

Subject(s)

Cryptography
Computer security
Filsafat
Number theory

Specific Detail Info

-

Statement of Responsibility

Samuel S. Wagstaff

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