Enhancements of Trapdoor Permutations Article

First Online: 13 September 2012 Received: 03 August 2011 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
Abstract 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 Communicated by Ran Canetti.

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© International Association for Cryptologic Research 2012

Authors and Affiliations 1. Department of Computer Science Weizmann Institute of Science Rehovot Israel