A Course in Number Theory and Cryptography

Inhaltsverzeichnis

• I. Some Topics in Elementary Number Theory.
• §1. Time estimates for doing arithmetic.
• §2. Divisibility and the Euclidean algorithm.
• §3. Congruences.
• §4. Some applications to factoring.
• II. Finite Fields and Quadratic Residues.
• §1. Finite fields.
• §2. Quadratic residues and reciprocity.
• III. Cryptography.
• §1. Some simple cryptosystems.
• §2. Enciphering matrices.
• IV. Public Key.
• §1. The idea of public key cryptography.
• §2. RSA.
• §3. Discrete log.
• §4. Knapsack.
• V. Primality and Factoring.
• §1. Pseudoprimes.
• §2. The rho method.
• §3. Fermat factorization and factor bases.
• §4. The continued fraction method.
• VI. Elliptic Curves.
• §1. Basic facts.
• §2. Elliptic curve cryptosystems.
• §3. Elliptic curve factorization.
• Answers to Exercises.