# Diffie-Hellman Assumption

I'm wondering if the following problem is as hard as computational or decision Diffie-Hellman problem? (Or is it actually an easy problem because $$c$$ is available?)

Given a cyclic group $$G$$ and let its order be $$q$$. Given $$g$$, $$q$$, $$g^a$$ and $$g^b$$ and $$c \in Z_q$$, decide if $$c \equiv a*b \mod q$$.

Another version of the problem could be: let $$G$$ be a group of unknown order (e.g., where RSA or strong RSA assumption could apply, thus computing roots would be hard).

• I assume we are given $g$ and $q$.
– fgrieu
Jul 9 at 21:27
• This problem is obviously no harder than DDH (given an Oracle that can solve DDH, it's easy to solve your problem) Jul 9 at 21:28
• Yes, given g and q. I have rephrased question correspondingly. Thanks!
– Sean
Jul 9 at 23:52