A new approach for electronic sealed-bid auctions that preserve the privacy of losing bids is presented. It reduces the number of operations performed by the auctioneers to O(log ); previous protocols require O(N ) or O(N log ) where the number of bidders is N and that of available bidding prices is . Namely, the number of auctioneers' operations in our auction protocol is independent of the number of bidders. This feature offers strong advantages in massive auctions. We also propose a new scheme that checks the equality of two values without disclosing them. The scheme enhances our basic auction protocol, in terms of security and communication costs.

The need for electronic sealed-bid auction services with quantitative competition is increasing. This paper proposes a new method that combines one-way functions and a bit commitment technique for quantitative competitive sealed-bid auctions. Since each modular exponentiation is replaced with a one-way function, the proposed method's computational time is one forty thousandth that of the former methods and the proposed method suits mass bidder systems.

This paper presents the results of the best differential characteristic search of FEAL. The search algorithm for the best differential characteristic (best linear expression) was already presented by Matsui, and improvements on this algorithm were presented by Moriai et al. We further improve the speed of the search algorithm. For example, the search time for the 7-round best differential characteristic of FEAL is reduced to about 10 minutes (Pentium/166 MHz), which is about 212. 6 times faster than Matsui's algorithm. Moreover, we determine all the best differential characteristics of FEAL for up to 32 rounds assuming all S-boxes are independent. As a result, we confirm that the N-round (7N32) best differential characteristic probability of FEAL is 2-2N, which was found by Biham. For N=6, we find 6-round differential characteristics with a greater probability, 2-11, than that previously discovered, 2-12.

This paper proposes an electronic soccer lottery protocol suitable for the Internet environment. Recently, protocols based on public-key schemes such as digital signature have been proposed for electronic voting systems or other similar systems. For a soccer lottery system in particular, it is important to reduce the computational complexity and the amount of communication data required, because we must expect that a large number of tickets will be purchased simultaneously. These problems can be solved by introducing hash functions as the core of protocol. This paper shows a practical soccer lottery system based on bit commitment and hash functions, in which the privacy of prize-winners is protected and illegal acts by the lottery promoter or lottery ticket shops can be revealed.

This paper proposes an extended variant of the method by Brickel et al. for multiple scalar multiplication over an elliptic curve. In smartcard environments, the proposed method is superior to conventional methods. In particular, when the typical number of bases t=2, the proposed method is four times faster than the simultaneous multiple exponentiation method, a well known fast method for multiple scalar multiplication. Furthermore, the proposed method can change the amount of time and memory to fit various platform environment (e.g., personal computers as rich ones or mobile devices such as smartcards as poor ones) by adjusting the division bit width (division unit).