As one form of electronic commerce, the scale of online trading in stocks is rapidly growing. Although brokers lie between the customers as trustees in the current market, retrenchment of broker seems inevitable. This paper proposes a protocol that allows trading to proceed with only the market and the customers. We show the required characteristics for this type of trading at first. Next, to fulfil these characteristics, we apply an electronic auction protocol and digital signatures. The result is a trading protocol with security equivalent to that the current trading system.

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 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 a bit-commitment scheme, BC(), and an efficient statistical zero-knowledge (in short, SZK) protocol in which, for any given multi-variable polynomial, f(X1,,Xt), and any given modulus, n, a prover, P, gives (I1,,It) to a verifier,ν, and can convince ν that P knows (x1,,xt) which satisfies f(x1,,xt) 0 (mod n) and Ii = BC(xi), (i = 1,,t). The proposed protocol is O(|n|) times more efficient than the corresponding previous ones. The (knowledge) soundness of our protocol holds under a computational assumption, the intractability of a modified RSA problem (see Def. 3.2), while the (statistical) zero-knowledgeness of the protocol needs no computational assumption. The protocol can be employed to construct various practical cryptographic protocols, such as fair exchange, untraceable electronic cash and verifiable secret sharing protocols.