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International Forum on Information Technology and Applications

Non-interactive Oblivious Transfer Protocols

Jing Qin, Zhao Huawei, Mingqiang Wang

Published May 1, 2009• 3 citations
Publisher

Abstract

Two novel constructions of one out of n oblivious transfer protocols from bilinear maps between groups are proposed. The protocols satisfy the category of non-interactive, mean that any sender S can obliviously transfer some secret(s) to a receiver R, but R does not send any messages back to S. The choice of a receiver is unconditionally secure. A sender's secrecy is guaranteed if the receiver is semi-honest in a standard model since the decision bilinear Diffie-Hellman problem is hard and the sender's secrecy is achieved when the receiver is a malicious party in a random oracle model since the bilinear Diffie-Hellman problem assumption holds. When a sender is a cheating party, the receiver will detect him/her and halt the protocol. A precise proof of the security of the protocols is presented.

DOI
10.1109/ifita.2009.180

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Two novel constructions of one out of n oblivious transfer protocols from bilinear maps between groups are proposed. The protocols satisfy the category of non-interactive, mean that any sender S can obliviously transfer some secret(s) to a receiver R, but R does not send any messages back to S. The choice of a receiver is unconditionally secure. A sender's secrecy is guaranteed if the receiver is semi-honest in a standard model since the decision bilinear Diffie-Hellman problem is hard and the sender's secrecy is achieved when the receiver is a malicious party in a random oracle model since the bilinear Diffie-Hellman problem assumption holds. When a sender is a cheating party, the receiver will detect him/her and halt the protocol. A precise proof of the security of the protocols is presented.
T wo non-interactive three parties k out of n oblivious transfer protocols from bilinear pairings are proposed i n this paper. In these protocols , a sender can obliviously transfer n messages to a receiver without communication with him/her. The public keys that a sender used to encrypt his/her messages are made by a third party. The receiver can extract k out of n messages at his/her choices by using the corresponding secret keys. The choices of the receiver are unconditionally secure. The sender's secrecy is guaranteed if the receiver is semi-honest in the standard model since the decision bilinear Diffie-Hellman problem (DBDH) is hard and the sender's secrecy is achieved when the receiver is a malicious party in the random oracle model since the bilinear Diffie-Hellman problem assumption (BDHA) holds. When a sender is a cheating party, the receiver will detect him/her and halt the protocol. A precise proof of the security of the protocols is presented.
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.
Abstract: 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, andS 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 OT k n 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, onlyO(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].
In an adaptive oblivious transfer (OT) protocol, a sender commits to a database of messages and then repeatedly interacts with a receiver in such a way that the receiver obtains one message per interaction of his choice (and nothing more) while the sender learns nothing about any of the choices. Recently, there has been significant effort to design practical adaptive OT schemes and to use these protocols as a building block for larger database applications. To be well suited for these applications, the underlying OT protocol should: (1) support an efficient initialization phase where one commitment can support an arbitrary number of receivers who are guaranteed of having the same view of the database, (2) execute transfers in time independent of the size of the database, and (3) satisfy a strong notion of security under a simple assumption in the standard model. We present the first adaptive OT protocol simultaneously satisfying these requirements. The sole complexity assumption required is that given (g, g a, g b, g c, Q), where g generates a bilinear group of prime order p and a, b, c are selected randomly from Zp, it is hard to decide if Q = g abc. All prior protocols in the standard model either do not meet our efficiency requirements or