Designs, Codes and Cryptography

, Volume 1, Issue 1, pp 47–62

Computation of discrete logarithms in prime fields

  • B. A. LaMacchia
  • A. M. Odlyzko

DOI: 10.1007/BF00123958

Cite this article as:
LaMacchia, B.A. & Odlyzko, A.M. Des Codes Crypt (1991) 1: 47. doi:10.1007/BF00123958


The presumed difficulty of computing discrete logarithms in finite fields is the basis of several popular public key cryptosystems. The secure identification option of the Sun Network File System, for example, uses discrete logarithms in a field GF(p) with p a prime of 192 bits. This paper describes an implementation of a discrete logarithm algorithm which shows that primes of under 200 bits, such as that in the Sun system, are very insecure. Some enhancements to this system are suggested.

Copyright information

© Kluwer Academic Publishers 1991

Authors and Affiliations

  • B. A. LaMacchia
    • 1
  • A. M. Odlyzko
    • 2
  1. 1.Massachusetts Institute of TechnologyCambridgeUSA
  2. 2.AT&T Bell LaboratoriesMurray HillUSA

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