I'm wondering what is the current knowledge regarding the difficulty of solving the Diffie-Hellman problem (DHP).
Obvisously solving the DLP (discrete log) is at least as hard as solving the DH problem.
What about the converse :
- In a general setting (cyclic group, no other assumption) ?
- With specific groups (multiplicative groups of finite fields, various EC, ...) ?
I found ftp://ftp.inf.ethz.ch/pub/crypto/publications/MauWol00c.pdf discussing the matter but this paper is more than 20 years old so I guess it might be outdated...