Computational number theory

Description

Content: Arithmetic of Integers Basic Arithmetic Operations GCD Congruences and Modular Arithmetic Linear Congruences Polynomial Congruences Quadratic Congruences Multiplicative Orders Continued Fractions Prime Number Theorem and Riemann Hypothesis Running Times of Arithmetic Algorithms Arithmetic of Finite Fields Existence and Uniqueness of Finite Fields Representation of Finite Fields Implementation of Finite Field Arithmetic Some Properties of Finite Fields Alternative Representations of Finite Fields Computing Isomorphisms among Representations Arithmetic of Polynomials Polynomials over Finite Fields Finding Roots of Polynomials over Finite Fields Factoring Polynomials over Finite Fields Properties of Polynomials with Integer Coefficients Factoring Polynomials with Integer Coefficients Arithmetic of Elliptic Curves Gaussian Elimination Lanczos Method Wiedemann Method Block Methods Public-Key Cryptography Public-Key Encryption Key Agreement Digital Signatures Entity Authentication Pairing-Based Cryptography Appendix A: Background Appendix B: Solutions to Selected Exercises Index