caa a22 4500 475807510 CHVBK 20180406123751.0 cr unu---uuuuu 170329e20000301xx s 000 0 eng 10.1023/A:1008350005447 doi (NATIONALLICENCE)springer-10.1023/A:1008350005447 Odlyzko Andrew AT&T Labs - Research, USA aut Discrete Logarithms: The Past and the Future [Elektronische Daten] [Andrew Odlyzko] The first practical public key cryptosystem to be published, the Diffie-Hellman key exchange algorithm, was based on the assumption that discrete logarithms are hard to compute. This intractability hypothesis is also the foundation for the presumed security of a variety of other public key schemes. While there have been substantial advances in discrete log algorithms in the last two decades, in general the discrete log still appears to be hard, especially for some groups, such as those from elliptic curves. Unfortunately no proofs of hardness are available in this area, so it is necessary to rely on experience and intuition in judging what parameters to use for cryptosystems. This paper presents a brief survey of the current state of the art in discrete logs. Kluwer Academic Publishers, 2000 discrete logarithms nationallicence Diffie- nationallicence Hellman key exchange nationallicence number field sieve nationallicence Designs, Codes and Cryptography Kluwer Academic Publishers 19/2-3(2000-03-01), 129-145 0925-1022 19:2-3<129 2000 19 10623 https://doi.org/10.1023/A:1008350005447 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1008350005447 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Odlyzko Andrew AT&T Labs - Research, USA aut NATIONALLICENCE 773 0- Designs, Codes and Cryptography Kluwer Academic Publishers 19/2-3(2000-03-01), 129-145 0925-1022 19:2-3<129 2000 19 10623 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer