Computational number theory

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.