Irreducibility to the One-More Evaluation Problems: More May Be Less

For a random-self-reducible function, the evaluation problem is irreducible to the one-moreevaluation problem, in the following sense. An irreduction algorithm exists that, given a re-duction algorithm from the evaluation to the one-more evaluation problem, solves a separatorproblem: the evaluation problem itself. Another irreduction shows that if the computationalDiffie-Hellman problem is reduced to the gap Diffie-Hellman problem, then the decision Diffie-Hellman problem is easy. Irreductions are primarily of theoretical interest, because they donot actually prove inequivalence between problems. What these irreductions suggest, though,is that one-more variants of the RSA and discrete logarithm problems may be easier than thestandard variants, and that the gap Diffie-Hellman problem may be easier than the standardDiffie-Hellman problem.