Annual International Conference on the Theory and Applications of Cryptographic Techniques

EUROCRYPT 2005: Advances in Cryptology – EUROCRYPT 2005 pp 78-95

Smooth Projective Hashing and Two-Message Oblivious Transfer

  • Yael Tauman Kalai
Conference paper

DOI: 10.1007/11426639_5

Volume 3494 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Kalai Y.T. (2005) Smooth Projective Hashing and Two-Message Oblivious Transfer. In: Cramer R. (eds) Advances in Cryptology – EUROCRYPT 2005. EUROCRYPT 2005. Lecture Notes in Computer Science, vol 3494. Springer, Berlin, Heidelberg


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). Our framework is actually 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 N’th-Residuosity Assumption, and the security of the other is based on both the Quadratic Residuosity Assumption and the Extended Riemann Hypothesis. Our security guarantees are not simulation based, and are similar to those of previous constructions.

When using smooth projective hashing in this context, we must deal with maliciously chosen smooth projective hash families. This raises new technical difficulties, and in particular it is here that the Extended Riemann Hypothesis comes into play.

Download to read the full conference paper text

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Yael Tauman Kalai
    • 1
  1. 1.Massachusetts Institute of Technology