A Course in Number Theory and Cryptography von Neal Koblitz | ISBN 9781468403107

A Course in Number Theory and Cryptography

von Neal Koblitz
Buchcover A Course in Number Theory and Cryptography | Neal Koblitz | EAN 9781468403107 | ISBN 1-4684-0310-9 | ISBN 978-1-4684-0310-7

A Course in Number Theory and Cryptography

von Neal Koblitz

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.