Journal of Cryptology

, Volume 26, Issue 3, pp 484-512

First online:

Enhancements of Trapdoor Permutations

  • Oded GoldreichAffiliated withDepartment of Computer Science, Weizmann Institute of Science
  • , Ron D. RothblumAffiliated withDepartment of Computer Science, Weizmann Institute of Science Email author 

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We take a closer look at several enhancements of the notion of trapdoor permutations. Specifically, we consider the notions of enhanced trapdoor permutation (Goldreich, Foundation of Cryptography: Basic Applications, 2004) and doubly enhanced trapdoor permutation (Goldreich, Computational Complexity: A Conceptual Perspective, 2011) as well as intermediate notions (Rothblum, A Taxonomy of Enhanced Trapdoor Permutations, 2010). These enhancements arose in the study of Oblivious Transfer and NIZK, but they address natural concerns that may arise also in other applications of trapdoor permutations. We clarify why these enhancements are needed in such applications, and show that they actually suffice for these needs.

Key words

Trapdoor permutations Oblivious transfer Non-interactive zero-knowledge