A Note on Chosen-Basis Decisional Diffie-Hellman Assumptions

  • Michael Szydlo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4107)


This note discusses two Decisional Diffie-Hellman assumption variants introduced by Abdalla and Pointcheval at Financial Cryptography’ 05. Those authors introduce two new problems and associated assumptions called the Chosen-Basis Decisional Diffie-Hellman assumption #1 (CDDH1), and the Chosen-Basis Decisional Diffie-Hellman assumption #2 (CDDH2), and suggest that these assumptions warrant further analysis. The problems are each defined in terms of a formal experiment, and advantage function, and the assumption is that an adversary should have negligible advantage. However, in this note, we exhibit a simple adversary for each problem, such that the advantage is significant. These new assumptions were motivated by the requirements of a proof of security for a three-party password authentication scheme described by the same authors. We conclude that the level of security assurance provided by this scheme is an open question.


Chosen basis Decisional Diffie-Hellman Interactive assumptions 


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  1. 1.
    Abdalla, M., Pointcheval, D.: Interactive Diffie-Hellman Assumptions With Applications to Password-Based Authentication. In: S. Patrick, A., Yung, M. (eds.) FC 2005. LNCS, vol. 3570, pp. 341–356. Springer, Heidelberg (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Michael Szydlo
    • 1
  1. 1.RSA LaboratoriesBedfordUSA

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