Section 6.1. Introduction
Section 6.2. Congruences and Residue Classes
Section 6.3. Euler's Phi Function
Section 6.4. The Theorems of Fermat, Euler and Lagrange
Section 6.5. Quadratic Residues
Section 6.6. Square Roots Modulo Integer
Section 6.7. Blum Integers
Section 6.8. Chapter Summary
Exercises

Leading HP security expert Wenbo Mao explains why "textbook" crypto schemes, protocols, and systems are profoundly vulnerable by revealing real-world-scenario attacks. Next, he shows how to realize cryptographic systems and protocols that are truly "fit for application"--and formally demonstrates their fitness. Mao presents practical examples throughout and provides all the mathematical background you'll need.



Coverage includes:

Crypto foundations: probability, information theory, computational complexity, number theory, algebraic techniques, and more
Authentication: basic techniques and principles vs. misconceptions and consequential attacks
Evaluating real-world protocol standards including IPSec, IKE, SSH, TLS (SSL), and Kerberos
Designing stronger counterparts to vulnerable "textbook" crypto schemes
Mao introduces formal and reductionist methodologies to prove the "fit-for-application" security of practical encryption, signature, signcryption, and authentication schemes. He gives detailed explanations for zero-knowledge protocols: definition, zero-knowledge properties, equatability vs. simulatability, argument vs. proof, round-efficiency, and non-interactive versions.