I want to give an introductory talk on Diffie-Helman key exchange. Along the way, I will mention that there exist groups, like $(\mathbb Z/p\mathbb Z)^\times$ for which it is believed that the discrete logarithm problem (DLP) is hard. Trying to anticipate a question from the audience, suppose someone asks:
Are there groups for which the DLP is surely known to be hard?
What is a good way to answer such a question, and in the case of no asnwer, how do I convince the audience that the Diffie-Helman key exchange is still worth the hustle? I understand this is not good question to ask here, so I bring my honest apologies.