I understand that in Diffie-Hellman it should be hard to compute $a$ given $g$ and $g^a$.

In computational Diffie-Hellam, it appears to be hard to compute $(g^{ab})$ from $g^a$ and $g^b$.

Is it also difficult to compute the discrete log of more trivial things, such as $g^a+1$, given $g^a$ and $a$? Or the discrete log of $(g^a+1)^b$ given $a$ and $b$?

Many thanks!

edit: I always mean discrete log with base $g$

I understand that in Diffie-Hellman it should be hard to compute $a$ given $g$ and $g^a$.

In computational Diffie-Hellman, it appears to be hard to compute $(g^{ab})$ from $g^a$ and $g^b$.

As for the field, please consider $\mathbb F_p^*$ for this question.

Is it also difficult to compute the discrete log $w$ of more trivial things, such as $g^w\equiv (g^a+1)^b\pmod p$? It may be assumed that $a,b,g$ and $p$ are given.

I understand that in Diffie-Hellman it should be hard to compute $a$ given $g$ and $g^a$.

In computational Diffie-Hellam, it appears to be hard to compute $(g^{ab})$ from $g^a$ and $g^b$.

Is it also difficult to compute the discrete log of more trivial things, such as $g^a+1$, given $g^a$ and $a$? Or the discrete log of $(g^a+1)^b$ given $a$ and $b$?

Many thanks!

I understand that in Diffie-Hellman it should be hard to compute $a$ given $g$ and $g^a$.

In computational Diffie-Hellam, it appears to be hard to compute $(g^{ab})$ from $g^a$ and $g^b$.

Is it also difficult to compute the discrete log of more trivial things, such as $g^a+1$, given $g^a$ and $a$? Or the discrete log of $(g^a+1)^b$ given $a$ and $b$?

Many thanks!

edit: I always mean discrete log with base $g$