Table of contents 1. Cyberspace Security and Cryptography 2. Mathematical Preliminaries 3. Computational Preliminaries 4. Secret-Key Cryptography 5. Factoring Based Cryptography 6. Logarithm Based Cryptography 7. Elliptic Curve Cryptography 8. Quantum Safe Cryptography 9. Offensive Cryptography 10. Back Matter
CONTENTS: Computational/mathematical preliminaries Computacility, complexity and intractability Efficient number-theoretic algoeithms RSA public-key cryptography RSA-type cryptosystems INteger factorization attacks Quadratic sieve attack Number field sieve attack Discrete logarithm attacks Index calculus attacks Xedni calculus attack Qunatum computing attacks Simple ele…
This book provides a comprehensive introduction to advanced topics in the computational and algorithmic aspects of number theory, focusing on applications in cryptography. Readers will learn to develop fast algorithms, including quantum algorithms, to solve various classic and modern number theoretic problems. Key problems include prime number generation, primality testing, integer factorizatio…
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 …