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Black-Box Separations for One-More (Static) CDH and Its Generalization

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNSC,volume 8874)

Abstract

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.

Keywords

  • Blind Signature
  • Test Algorithm
  • Security Parameter
  • Discrete Logarithm Problem
  • Impossibility Result

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Jiang Zhang, Zhenfeng Zhang and Yanfei Guo are sponsored by the National Basic Research Program of China under Grant No. 2013CB338003, and the National Natural Science Foundation of China (NSFC) under Grant No. 61170278, 91118006. Yu Chen is sponsored by NSFC under Grant No. 61303257, and the Strategic Priority Research Program of CAS under Grant No. XDA06010701. Zongyang Zhang is an International Research Fellow of JSPS and his work is in part supported by NSFC under grant No. 61303201.

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Zhang, J., Zhang, Z., Chen, Y., Guo, Y., Zhang, Z. (2014). Black-Box Separations for One-More (Static) CDH and Its Generalization. In: Sarkar, P., Iwata, T. (eds) Advances in Cryptology – ASIACRYPT 2014. ASIACRYPT 2014. Lecture Notes in Computer Science, vol 8874. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45608-8_20

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  • DOI: https://doi.org/10.1007/978-3-662-45608-8_20

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