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arXiv:0909.2852

A new efficient k-out-of-n Oblivious Transfer protocol

Ashwin Jain, C. Hari

Published Sep 15, 2009• 1 citation
arXivHTMLPDF

Abstract

This paper presents a new efficient protocol for k-out-of-n oblivious transfer which is a generalization of Parakh's 1-out-of-2 oblivious transfer protocol based on Diffie-Hellman key exchange. In the proposed protocol, the parties involved generate Diffie-Hellman keys obliviously and then use them for oblivious transfer of secrets.
DOI
10.48550/arxiv.0909.2852

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Key-exchange protocols have been overlooked as a possible means for implementing oblivious transfer (OT). In this article, we present protocols for mutual exchange of secrets, 1-out-of-2 OT and coin-flipping similar to the Diffie-Hellman protocol using the idea of obliviously exchanging encryption keys. Since the Diffie-Hellman scheme is widely used, our protocol may provide a useful alternative to the conventional methods for implementation of oblivious transfer and a useful primitive in building larger cryptographic schemes.
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].
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].
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.
Oblivious Transfer (OT) is the fundamental building block of cryptographic protocols. In this paper we describe the simplest and most efficient protocol for 1-out-of- n OT to date, which is obtained by tweaking the Diffie-Hellman key-exchange protocol. The protocol achieves UC-security against active and adaptive corruptions in the random oracle model. Due to its simplicity, the protocol is extremely efficient and it allows to perform m 1-out-of- n OTs using only: Computation: (n+1)m+2(n+1)m+2(n+1)m+2 exponentiations ( mn for the receiver, mn+2mn+2mn+2 for the sender) and Communication: 32(m+1)32(m+1)32(m+1) bytes (for the group elements), and 2 mn ciphertexts. We also report on an implementation of the protocol using elliptic curves, and on a number of mechanisms we employ to ensure that our software is secure against active attacks too. Experimental results show that our protocol (thanks to both algorithmic and implementation optimizations) is at least one order of magnitude faster than previous work. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.