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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

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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
Number theory

Specific Detail Info

-

Statement of Responsibility

Samuel S. Wagstaff

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