Paper 2007/435 Original: eprint.iacr.org/2007/435 ↗

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

Abstract

For a random-self-reducible function, the evaluation problem is irreducible to the one-more evaluation problem, in the following sense. An irreduction algorithm exists that, given a reduction algorithm from the evaluation to the one-more evaluation problem, solves a separator problem: the evaluation problem itself. Another irreduction shows that if the computational Diffie-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 do not 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 the standard variants, and that the gap Diffie-Hellman problem may be easier than the standard Diffie-Hellman problem.