RECORD NO.: 3009255 INSPEC Abstract No: B87069025; C87065973
AUTHOR: Odlyzko, A.M.
EDITOR: Beth, T.; Cot, N.; Ingemarsson, I.
CORP SOURCE: AT&T Bell Labs., Murray Hill, NJ, USA
TITLE: Discrete logarithms in finite fields and their cryptographic
significance
SOURCE: Advances in Cryptology. Proceedings of EUROCRYPT 84 - A
Workshop on the Theory and Application of Cryptographic
Techniques, p. vii+489, 224-314
PLACE OF PUBL: West Germany
TRANSLATED IN: B02
ISBN: 3540160760
LANGUAGE: English
PUBLISHER: Springer-Verlag; Berlin, West Germany
SPONSOR ORG: Int. Assoc. Cryptographic Res.; UER Maths., Logique
Formelle, Inf
CONF LOCATION: Paris, France; 9-11 April 1984
YEAR: 1985
TREATMENT: B Bibliography; T Theoretical or Mathematical
ABSTRACT: Given a primitive element g of a finite field GF(q), the
discrete logarithm of a nonzero element u in GF(q) is that
integer k, 1<or=k<or=q-1, for which u=g/sup k/. The well-
known problem of computing discrete logarithms in finite
fields has acquired additional importance in recent years
due to its applicability in cryptography. Several
cryptographic systems would become insecure if an efficient
discrete logarithm were discovered. The author surveys and
analyzes known algorithms in this area, with special
attention devoted to algorithms for the fields GF(2/sup n/).
It appears that in order to be safe from attacks using these
algorithms, the value of n for which GF(2/sup n/) is used in
a cryptosystem has to be very large and carefully chosen.
Due in large part to recent discoveries, discrete logarithms
in fields GF(2/sup n/) are much easier to compute than in
fields GF(p) with p prime. Hence the fields GF(2/sup n/)
ought to be avoided in all cryptographic applications. On
the other hand, the fields GF(p) with p prime appear to
offer relatively high levels of security (72 Refs.)
DESCRIPTORS: cryptography
IDENTIFIERS: finite fields; cryptographic significance; discrete
logarithm; nonzero element; cryptography
CLASS CODES: B6120B (Codes); C6130 (Data handling techniques)