Journal of Cryptology

, Volume 26, Issue 3, pp 484–512

Enhancements of Trapdoor Permutations


DOI: 10.1007/s00145-012-9131-8

Cite this article as:
Goldreich, O. & Rothblum, R.D. J Cryptol (2013) 26: 484. doi:10.1007/s00145-012-9131-8


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 

Copyright information

© International Association for Cryptologic Research 2012

Authors and Affiliations

  1. 1.Department of Computer ScienceWeizmann Institute of ScienceRehovotIsrael

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