Black-Box Separations for One-More (Static) CDH and Its Generalization
As one-more problems are widely used in both proving and analyzing the security of various cryptographic schemes, it is of fundamental importance to investigate the hardness of the one-more problems themselves. Bresson et al. (CT-RSA ’08) first showed that it is difficult to rely the hardness of some one-more problems on the hardness of their “regular” ones. Pass (STOC ’11) then gave a stronger black-box separation showing that the hardness of some one-more problems cannot be based on standard assumptions using black-box reductions. However, since previous works only deal with one-more problems whose solution can be efficiently checked, the relation between the hardness of the one-more (static) CDH problem over non-bilinear groups and other hard problems is still unclear. In this work, we give the first impossibility results showing that black-box reductions cannot be used to base the hardness of the one-more (static) CDH problem (over groups where the DDH problem is still hard) on any standard hardness assumption. Furthermore, we also extend the impossibility results to a class of generalized “one-more” problems, which not only subsume/strengthen many existing separations for traditional one-more problems, but also give new separations for many other interesting “one-more” problems.
KeywordsBlind Signature Test Algorithm Security Parameter Discrete Logarithm Problem Impossibility Result
Unable to display preview. Download preview PDF.
- 11.Brown, D.R.L.: Irreducibility to the one-more evaluation problems: More may be less. Cryptology ePrint Archive, Report 2007/435 (2007)Google Scholar
- 12.Brown, D.R.L., Gallant, R.P.: The static Diffie-Hellman problem. Cryptology ePrint Archive, Report 2004/306 (2004)Google Scholar
- 15.Canetti, R., Lin, H., Pass, R.: Adaptive hardness and composable security in the plain model from standard assumptions. In: FOCS, pp. 541–550 (2010)Google Scholar
- 17.Chaum, D.: Blind signatures for untraceable payments. In: CRYPTO, pp. 199–203 (1982)Google Scholar
- 20.Deng, Y., Goyal, V., Sahai, A.: Resolving the simultaneous resettability conjecture and a new non-black-box simulation strategy. In: FOCS, pp. 251–260 (2009)Google Scholar
- 28.Gentry, C., Wichs, D.: Separating succinct non-interactive arguments from all falsifiable assumptions. In: STOC, pp. 99–108 (2011)Google Scholar
- 34.Koblitz, N., Menezes, A.: Another look at non-standard discrete log and Diffie-Hellman problems. Cryptology ePrint Archive, Report 2007/442 (2007)Google Scholar
- 37.Pass, R.: Limits of provable security from standard assumptions. In: STOC, pp. 109–118 (2011)Google Scholar
- 40.Prabhakaran, M., Rosen, A., Sahai, A.: Concurrent zero knowledge with logarithmic round-complexity. In: FOCS, pp. 366–375 (2002)Google Scholar