Enhancements are Blackbox Non-trivial: Impossibility of Enhanced Trapdoor Permutations from Standard Trapdoor Permutations

  • Mohammad HajiabadiEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11239)


Trapdoor permutations (TDP) are a fundamental primitive in cryptography. Several variants of this notion have emerged as a result of different applications. However, it is not clear whether these variants can be based on the standard notion of TDPs.

We study the question of whether enhanced trapdoor permutations can be based on classical trapdoor permutations. The main motivation of our work is in the context of existing TDP-based constructions of oblivious transfer and non-interactive zero knowledge protocols, which require enhancements to the classical TDP notion. We prove that these enhancements are non-trivial, in the sense that there does not exist fully blackbox constructions of enhanced TDPs from classical TDPs.

On the technical side, we show that the enhanced TDP security of any construction in the random TDP oracle world can be broken via a polynomial number of queries to the TDP oracle as well as a weakening oracle, which provides inversion with respect to randomness. We also show that the standard one-wayness of the random TDP oracle stays intact in the presence of this weakening oracle.



I am grateful to the anonymous reviewers for their useful comments, and especially to one reviewer for their very elaborate comments. I would also like to thank Bruce Kapron for commenting on an earlier draft of the paper.


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Copyright information

© International Association for Cryptologic Research 2018

Authors and Affiliations

  1. 1.University of California BerkeleyBerkeleyUSA
  2. 2.University of VirginiaCharlottesvilleUSA

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