TY - JOUR
T1 - Discrete Logarithms
T2 - The Past and the Future
AU - Odlyzko, Andrew
PY - 2000/3
Y1 - 2000/3
N2 - 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.
AB - 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.
KW - Diffie-Hellman key exchange
KW - Discrete logarithms
KW - Number field sieve
UR - http://www.scopus.com/inward/record.url?scp=0001534053&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0001534053&partnerID=8YFLogxK
U2 - 10.1023/A:1008350005447
DO - 10.1023/A:1008350005447
M3 - Article
AN - SCOPUS:0001534053
SN - 0925-1022
VL - 19
SP - 129
EP - 145
JO - Designs, Codes, and Cryptography
JF - Designs, Codes, and Cryptography
IS - 2-3
ER -