The question is quite simple:

**Is there a group where solving the CDH problem can be shown to be easy but solving the discrete logarithm problem is assumed to be hard?**

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**Refresher on the problems:**

* **CDH:** Let $\mathbb G=(G,+,0,p)$ be a public cyclic group of order $p$. Given any $g\in G$ and $g^a,g^b$ with $a,b\stackrel{\$}{\gets}\{0,\ldots,p-1\}$, that is with uniformly random exponents, find $g^{ab}$.
* **DLog:** Let $\mathbb G=(G,+,0,p)$ be a public cyclic group of order $p$. Given any $g\in G$ and $g^a$ with $a\stackrel{\$}{\gets}\{0,\ldots,p-1\}$, that is with a uniformly random exponent, find $a$.