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A Course in Number Theory and Cryptography
von Neal KoblitzInhaltsverzeichnis
- 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.