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Cryptology

III.4 The Discrete Logarithm with Cryptographic Applications

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Contents

  1. The discrete logarithm [PDF]
  2. DIFFIE-HELLMAN key exchange [PDF]
  3. The man in the middle [PDF]
  4. Secret communication without key exchange [PDF]
  5. ELGAMAL cipher—idea [PDF]
  6. Computing discrete logarithms [PDF]

The complete chapter as PDF file


Overview

Computing discrete logarithms is believed—like factoring large integers—to be a hard problem. This serves as basis of many cryptographic procedures.

A useful aspect of most of these procedures is that they rely only on the group property of the multiplicative groups of the residue class rings of integers. Therefore they often have an immediate translation to other groups such as elliptic curves. Should discrete logarithms for residue class rings happen to be efficiently computable there remains a chance that the procedures remain secure for other groups.


Author: Klaus Pommerening, 2000-Jun-29; last change: 2021-Feb-15.