E-Book, Englisch, 520 Seiten
Reihe: Chapman & Hall/CRC Cryptography and Network Security Series
E-Book, Englisch, 520 Seiten
Reihe: Chapman & Hall/CRC Cryptography and Network Security Series
ISBN: 978-1-4200-7003-3
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
Divided into three parts, the book begins with a short introduction to cryptography and a background chapter on elementary number theory and algebra. It then moves on to algorithms, with each chapter in this section dedicated to a single topic and often illustrated with simple cryptographic applications. The final part addresses more sophisticated cryptographic applications, including LFSR-based stream ciphers and index calculus methods.
Accounting for the impact of current computer architectures, this book explores the algorithmic and implementation aspects of cryptanalysis methods. It can serve as a handbook of algorithmic methods for cryptographers as well as a textbook for undergraduate and graduate courses on cryptanalysis and cryptography.
Zielgruppe
Mathematicians and computer scientists in cryptography, discrete mathematics, and algorithms.
Autoren/Hrsg.
Weitere Infos & Material
BACKGROUND
A Bird’s-Eye View of Modern Cryptography
Preliminaries
Defining security in cryptography
Elementary Number Theory and Algebra Background
Integers and rational numbers
Greatest common divisors in Z
Modular arithmetic
Univariate polynomials and rational fractions
Finite fields
Vectors spaces and linear maps
The RSA and Diffie–Hellman cryptosystems
ALGORITHMS
Linear Algebra
Introductory example: multiplication of small matrices over F2
Dense matrix multiplication
Gaussian elimination algorithms
Sparse linear algebra
Sieve Algorithms
Introductory example: Eratosthenes’s sieve
Sieving for smooth composites
Brute Force Cryptanalysis
Introductory example: dictionary attacks
Brute force and the DES algorithm
Brute force as a security mechanism
Brute force steps in advanced cryptanalysis
Brute force and parallel computers
The Birthday Paradox: Sorting or Not?
Introductory example: birthday attacks on modes of operation
Analysis of birthday paradox bounds
Finding collisions
Application to discrete logarithms in generic groups
Birthday-Based Algorithms for Functions
Algorithmic aspects
Analysis of random functions
Number theoretic applications
A direct cryptographic application in the context of blockwise security
Collisions in hash functions
Hellman’s time memory tradeoff
Birthday Attacks through Quadrisection
Introductory example: subset sum problems
General setting for reduced memory birthday attacks
Extensions of the technique
Some direct applications
Fourier and Hadamard–Walsh Transforms
Introductory example: studying S-boxes
Algebraic normal forms of boolean functions
Goldreich–Levin theorem
Generalization of the Walsh transform to Fp
Fast Fourier transforms
Lattice Reduction
Definitions
Introductory example: Gauss reduction
Higher dimensions
Shortest vectors and improved lattice reduction
Dual and orthogonal lattices
Polynomial Systems and Gröbner Bases Computations
General framework
Bivariate systems of equations
Definitions: multivariate ideals, monomial orderings, and Gröbner bases
Buchberger algorithm
Macaulay’s matrices
Faugère’s algorithms
Algebraic attacks on multivariate cryptography
On the complexity of Gröbner bases computation
APPLICATIONS
Attacks on Stream Ciphers
LFSR-based keystream generators
Correlation attacks
Algebraic attacks
Extension to some nonlinear shift registers
The cube attack
Time memory data tradeoffs
Lattice-Based Cryptanalysis
Direct attacks using lattice reduction
Coppersmith’s small roots attacks
Elliptic Curves and Pairings
Introduction to elliptic curves
The Weil pairing
The elliptic curve factoring method
Index Calculus Algorithms
Introduction to index calculus
A simple finite field example
Generalization to finite fields with small enough characteristics
Introduction to the number field sieve
Smoothness probabilities
References
