I've read our recent question: "One-time pad using RSA and Diffie-Hellman functions" which asks about the security of a particular way to convert RSA and discrete exponentiation into a stream cipher. The approach didn't work out, as expected, knowing that it was an interview question.
Now, the following question came over me:
Is it (constructively) possible to create a stream cipher whose IND-CPA security can be directly reduced to a well-known number-theoretic assumption?
To be clear: I'd like to know (out of curiosity, no deployment intended) whether there exists a stream cipher which is as hard to break as CDH (or another assumption) with no other assumptions (no random oracles, no constructed PRPs like AES, no constructed PRFs like SHA-2, ...) and if such a stream cipher can exist , I'd also like to know how to build it (e.g. give a brief description please).
Example assumptions: "factoring is hard", "the RSA problem is hard", DLOG, CDH, DDH