I am wondering whether there are any current challenge problems for Discrete Logarithms.
Specifically in $\mathbb{Z}_p^\ast$ as well as in elliptic curve groups.
It turns out CERTICOM still has some ECC challenges, and it seems 131 bits is the smallest unsolved case. See the link here.
One concern I have is that given the 109 bit challenge was solved in 2004, is it the case that 131 bits is still out of reach, or have people simply not been trying?
I suppose this question could also be restated (ignoring specific ECC details) as follows:
What is the longest bitlength that a generic discrete logarithm solution has been found for? I am thinking Baby Step Giant Step (but memory would be a problem) so maybe think of Pollard rho.
I am aware of the special exponent and small ground field breakthroughs, see for example the question here but this question is not about them.