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Advanced materials research

Analysis on A 1-out-n Security Protocol Based on Threshold Idea

Yu Li, Jun Yao Ye

Published Dec 1, 2012• 0 citations
Publisher

Abstract

In a 1-out-n oblivious transfer model, the sender sends n messages to the receiver. But the receiver can only get 1 message from the n messages, and the sender does not know which message the receiver has gotten. In this paper, we proposed a multiple-use 1-out-n oblivious transfer protocol based on threshold idea. It is more efficient than Naor-Pinkas protocol[1] and Tzeng protocol[2].

DOI
10.4028/www.scientific.net/amr.605-607.2329

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In a 1-out-n oblivious transfer model, the sender sends n messages to the receiver. But the receiver can only get 1 message from the n messages, and the sender does not know which message the receiver has gotten. In this paper, we proposed a multiple-use 1-out-n oblivious transfer protocol based on threshold idea. It is more efficient than Naor-Pinkas protocol[1] and Tzeng protocol[2].
Oblivious Transfer (OT) has been regarded as one of the most significant cryptography tools in recent decades.Since the mechanism of OT is widely used in many applications such as e-commerce, secret information exchange, and games, various OT schemes have been proposed to improve its functionality and efficiency.In 2001, Naor and Pinkas proposed a secure 1-out-of-n OT protocol, in which the sender has n messages and the chooser can get one of these n messages in each protocol run.What is more, the sender cannot find which message has been chosen by the chooser and the chooser knows only the correct message.In 2004, Wakaha and Ryota proposed a secure t-out-of-n OT protocol, which is an extension of the 1-out-of-n OT protocol proposed by Naor and Pinkas.Wakaha and Ryota's tout-of-n OT protocol allows the chooser to get t messages from the sender simultaneously in each protocol run.Besides, the sender cannot know what the chooser has chosen and the chooser can only know the exact t messages.However, getting deep understanding of Wakaha and Ryota's protocol, it could be concluded that it still lacks efficiency such that it is hard to be applied in real-world applications.In this article, a secure and efficient t-out-of-n OT protocol based on the Generalized Chinese Remainder Theorem is proposed, in which the chooser can securely get t messages from the sender simultaneously in each protocol run.The efficiency of the proposed t-out-of-n OT protocol is higher than that of Wakaha and Ryota's protocol in terms of practical application.
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].
In a t-out-n oblivious transfer, the receiver can only receive t messages out of n messages sent by the sender; and the sender has no idea about which ones have been received. Majority of the existing of previous efficient oblivious transfer schemes require t calls of 1-out-n oblivious transfer to construct the t-out-n oblivious transfer. Its computational requirements and bandwidth consumption are quite demanding. Therefore, to guarantee the quality of electronic commercial service, an efficient t-out-n oblivious transfer scheme is urgently desired. Based on the RSA, we propose a new t-out-n oblivious transfer protocol for private information retrieval in this paper. In our method, only several modular multiplications and t hash functions are performed by a user (receiver) to obtain t messages. It is very suitable for the limited computation capacities of receivers such as smart cards or mobile units. Key words: Private information retrieval, security, RSA
In this article, the authors cryptanalyze a k-out-of-n oblivious transfer protocol proposed in [12 Jain , A. , and C. Hari . 2010 . A New Efficient Protocol for k-out-of-n Oblivious Transfer , Cryptologia , 34 ( 4 ): 282 – 290 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]]. Their protocol is one of the most efficient k-out-of-n oblivious transfer protocols and is directly built from a 1-out-of-n oblivious transfer protocol. However, their analysis shows that the proposed k-out-of-n oblivious transfer protocol is insecure, though the primitive 1-out-of-n oblivious transfer protocol is secure. The weakness is that with high probability the receiver in their protocol can get all n secret messages encrypted by the sender. Finally, they fix the serious flaw and introduce an improved k-out-of-n oblivious transfer protocol without increasing any cost.
We propose a quantum protocol for 1-out-of-2, 1-out-of-n and k-out-of-n oblivious transfer. Oblivious transfer is a counter-intuitive cryptographic primitive in which the receiver receives only the information he is authorized for, while the sender does not know what information receiver received. In 1-out-of-2 oblivious transfer, Alice sends two bits to Bob who can choose only one of them to read, while Alice does not know which bit Bob read. k-out-of-n oblivious transfer is an extension of this idea. The proposed protocols do not require any classical communication, are practical, secure and can be implemented using current technology.