## Cryptology ePrint Archive: Report 2007/435

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

*Daniel R. L. Brown*

**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.

**Category / Keywords: **foundations / irreduction, one-more evaluation, gap DHP

**Date: **received 23 Nov 2007, last revised 9 Jun 2010

**Contact author: **dbrown at certicom com

**Available format(s): **Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation

**Note: **Minor changes.

**Version: **20100609:185708 (All versions of this report)

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