Computation of discrete logarithms in prime fields

B. A. LaMacchia, A. M. Odlyzko

Research output: Contribution to journalArticlepeer-review

54 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)47-62
Number of pages16
JournalDesigns, Codes and Cryptography
Issue number1
StatePublished - May 1991


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