Oblivious Comparator and Its Application to Secure Auction Protocol (特集:プライバシを保護するコンピュータセキュリティ技術)

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概要

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• This paper presents a protocol for Secure Function Evaluation (SFE) in which n players have secret inputs E[a_1], E[a_2],・・・, E[a_n], of a known boolean function f, and they collaborate to compute the ciphertext of the output of the boolean function, E[f(a_1,・・・,a_n)]. The main result is a completeness theorem (Theorem 3.1) which states that an arbitrary function can be evaluated at the oblivious party without help of private information. The proposed protocol is based on the Jakobsson and Juels's Mix-and-Match scheme (Jakobsson and Jules, 2000) in which the truth table of a target function is row-wise randomized (mixing) using a Mix network, and then players perform "matching" the designated output ciphertext and the corresponding rows. The biggest difference between the proposed SFE and the Mixand-Match is that the proposed protocol does not require any involvement of key holders to evaluate function, while the Mix-and-Match needs key holders to perform threshold decryptions at every step of evaluation of boolean gates. One disadvantage of the proposed scheme is the Reed-Muller expansion (Sasao, 1997) involves an exponential blow-up in the number of input, n, as the same as the conventional schemes, e.g., CyptoComputer proposed by Sander, Young, and Yung (1999). This paper presents an efficient construction for a primitive called ' oblivious comparator' with n-round complexity between the comparator and n players but the bandwidth spent by one communication is independent from n (linear to the size of values to be compared), and hence it does not suffer the blow-up in n. The oblivious comparator is suitable to implement a secure auction because an auctioneer communicates with bidders once at time, and performs evaluation without help of trusted key holders. In addition, the proposed construction allows arbitrary complicated functions including a search for second highest, a resolution the winner, and a dynamic programming (for combinatorial auction).

• 2004-08-15

著者

• Kikuchi H

  Department Of Information Media Technology School Of Information Technology And Electronics Tokai Un

• Kikuchi Hiroaki

  Department Electrical Engineering Tokai Univeristy

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• Oblivious Comparator and Its Application to Secure Auction Protocol (特集:プライバシを保護するコンピュータセキュリティ技術)
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