# Groups where discrete logarithm is hard

What are examples of groups, where DLP (discrete logarithm problem) is hard?

Two obvious ones are: integers modulo $p$ ($p$ being prime) and elliptic curves over finite fields. What are the others?

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Relevant: RSA Labs says "The best discrete logarithm algorithms [over finite fields] have expected running times similar to those of the best factoring algorithms." (link) – anon Sep 11 '11 at 11:12
As a point of clarification, you should distinguish between $\mathbb{Z}/p \mathbb{Z}$ and $(\mathbb{Z}/p \mathbb{Z})^ \times$. DLP is hard in the latter, and trivial in the former. – Brandon Carter Sep 11 '11 at 15:54
The difficulty of the discrete logarithm problem in a group is not a property of a group (that is, it is not invariant under isomorphism of groups); it is a property of a specific algorithm computing the group law using a specific algorithmic representation of the group's elements. – Qiaochu Yuan Jun 14 '12 at 9:35