Smooth Projective Hashing and Two-Message Oblivious Transfer

We present a general framework for constructing two-message oblivious transfer protocols using a modification of Cramer and Shoup’s notion of smooth projective hashing (2002). This k is an abstraction of the two-message oblivious transfer protocols of Naor and Pinkas (2001) and Aiello et al. (2001), whose security is based on the Decisional Diffie Hellman Assumption. In particular, we give two new oblivious transfer protocols. The security of one is based on the Quadratic Residuosity Assumption, and the security of the other is based on the N’th Residuosity Assumption. Our security guarantees are not simulation based, but are similar to the guarantees of the aforementioned two constructions. Compared to other applications of smooth projective hashing, in our context we must deal also with maliciously chosen parameters, which raises new technical difficulties. We also improve on prior constructions of factoring-based smooth universal hashing, in that our constructions do not requi...

• Type: Conference
• Year: 2005
• Where: EUROCRYPT
• Authors: Yael Tauman Kalai
• Keywords: Cryptography, EUROCRYPT 2005, Oblivious Transfer Protocols, Residuosity Assumption, Two-message Oblivious Transfer