Solving Diffie-Hellman vs DLP 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discussing the matter but this paper is more than 20 years old so I guess it might be outdated...
According to Wikipedia (with two articles sourced):

Computing the discrete logarithm is the only known method for solving the CDH problem. But there is no proof that it is, in fact, the only method. It is an open problem to determine whether the discrete log assumption is equivalent to the CDH assumption, though in certain special cases this can be shown to be the case.