Paper 2007/118

Smooth Projective Hashing and Two-Message Oblivious Transfer

Shai Halevi and Yael Tauman Kalai


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 framework 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. 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 require that the underlying RSA modulus is a product of safe primes*. (This holds for the schemes based on the Quadratic Residuosity Assumption as well as the ones based on the $N$'th Residuosity Assumption.) In fact, we observe that the safe-prime requirement is unnecessary for many prior constructions. In particular, the factoring-based CCA secure encryption schemes due to Cramer-Shoup, Gennaro-Lindell, and Camenisch-Shoup remain secure even if the underlying RSA modulus is not a product of safe primes.

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. Full version to appear in Journal of Cryptology
CCA-secure encryptionOblivious TransferSafe primesSmooth Projective Hashing
Contact author(s)
shaih @ alum mit edu
2010-10-31: revised
2007-04-03: received
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Creative Commons Attribution


      author = {Shai Halevi and Yael Tauman Kalai},
      title = {Smooth Projective Hashing and Two-Message Oblivious Transfer},
      howpublished = {Cryptology ePrint Archive, Paper 2007/118},
      year = {2007},
      note = {\url{}},
      url = {}
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