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International Conference on Security Technology (SecTech)

Efficient t-out-of-n Oblivious Transfer Schemes

Chin‐Chen Chang, Yeu‐Pong Lai

Published Dec 1, 2008• 3 citations
Publisher

Abstract

In this paper, we shall bring up two efficient t-out-of-n oblivious transfer schemes. The first comes out handy for communication and computation. However, it has a shortcoming in revealing combined information of secrets. To solve this problem, we have developed it into the second scheme.
DOI
10.1109/sectech.2008.19

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Oblivious transfer (OT) protocol is a fundamental cryptographical tool and widely used as a building block of secure computation. In this work, we propose two efficient t -out-of- n oblivious transfer schemes with the designated receiver. A common advantage of the two schemes is efficient. The total computation cost of the sender and the receiver is n +2 t +1 modular exponentiations in first scheme that is three-round, and the total one of the sender and receiver is n +3 t modular exponentiations in second scheme that is two-round. Another advantage of both schemes is designable.
A general approach for constructing t-out-n oblivious transfer is more practical than 1-out-n oblivious transfer for applications. To guarantee the quality of growing popular communication service, an efficient t-out-n oblivious transfer scheme is urgently desired. Based on the RSA and two-lock cryptosystem, we propose an efficient t-out-n oblivious transfer scheme in this paper. Compared with existing oblivious transfer schemes, our scheme can reduce many computations and communications for both the sender and the receiver. Moreover, our scheme is very suitable for smart-card users.
Oblivious transfer is an important cryptographic protocol in various security applications. For example, in on-line transactions, a k-out-of-n oblivious transfer scheme allows a buyer to privately choose k out of n digital goods from a merchant without learning information about other n-k goods. In this paper, we propose several efficient two-round k-out-of-n oblivious transfer schemes, in which the receiver R sends O(k) messages to the sender S, and S sends O(n) messages back to R. The schemes provide unconditional security for either sender or receiver. The computational security for the other side is based on the Decisional Diffie-Hellman (DDH) or Chosen-Target Computational Diffie-Hellman (CT-CDH) problems. Our schemes have the nice property of universal parameters, that is, each pair of R and S need not hold any secret before performing the protocol. The system parameters can be used by all senders and receivers without any trapdoor specification. In some cases, our OTkn schemes are the most efficient ones in terms of the communication cost, either in rounds or the number of messages. Moreover, one of our schemes is extended to an adaptive oblivious transfer scheme. In that scheme, S sends O(n) messages to R in one round in the commitment phase. For each query of R, only O(1) messages are exchanged and O(1) operations are performed. The preliminary version of this paper was published at PKC '05 [Chu and Tzeng 2005].
A new k-out-of-n oblivious transfer protocol is presented in this paper. The communication cost of our scheme are n+1 messages of sender to receiver and k messages from the receiver to sender. To the best knowledge of the authors, the communication complexity of our scheme is the least. Also, our scheme has a lower computation cost with (k+1)n modular exponentiations for sender and 3k modular exponentiations for the receiver. The security of our scheme is only based on the Decision Diffie-Hellman assumption. Further, we proved the sender’s computational security and the receiver’s unconditional security under standard model.