In an open-bid auction, a bidder can know the budgets of other bidders. Thus, a sealed-bid auction that hides bidding prices is desirable. However, in previous sealed-bid auction protocols, it has been difficult to provide a “fund binding” property, which would guarantee that a bidder has funds more than or equal to the bidding price and that the funds are forcibly withdrawn when the bidder wins. Thus, such protocols are vulnerable to a false bidding. As a solution, many protocols employ a simple deposit method in which each bidder sends a deposit to a smart contract, which is greater than or equal to the bidding price, before the bidding phase. However, this deposit reveals the maximum bidding price, and it is preferable to hide this information. In this paper, we propose a sealed-bid auction protocol that provides a fund binding property. Our protocol not only hides the bidding price and a maximum bidding price, but also provides a fund binding property, simultaneously. For hiding the maximum bidding price, we pay attention to the fact that usual Ethereum transactions and transactions for sending funds to a one-time address have the same transaction structure, and it seems that they are indistinguishable. We discuss how much bidding transactions are hidden. We also employ DECO (Zhang et al., CCS 2020) that proves the validity of the data to a verifier in which the data are taken from a source without showing the data itself. Finally, we give our implementation which shows transaction fees required and compare it to a sealed-bid auction protocol employing the simple deposit method.

Efficient general secure multiparty computation (MPC) protocols were previously proposed, and the combination with the efficient auction circuits achieves the efficient sealed-bid auctions with the full privacy and correctness. However, the combination requires that each bidder submits ciphertexts of bits representing his bid, and their zero-knowledge proofs. This cost amounts to about 80 multi-exponentiations in usual case that the bid size is 20 bits (i.e. about 1,000,000 bid prices). This paper proposes sealed-bid auction protocols based on the efficient MPC protocols, where a bidder can submit only a single ciphertext. The bidder's cost is a few multi-exponentiations, and thus the proposed protocols are suitable for mobile bidders. A novel technique for the realization is a bit-slicing conversion by multiple servers, where a single ciphertext for a bid is securely converted into ciphertexts of bits representing the bid.

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 proposes a secure electronic sealed-bid auction protocol (SEAP) that provides an auction service on the Internet by combining three providers: an auction service provider, a key service provider, and a time service provider. The SEAP uses public key cryptography and the concept of a time-key certificate. The most important property of this protocol is that time-dependent security requirements can be strictly satisfied. The SEAP satisfies the following nine security requirements: (a) no one can deny having made a bid; (b) the protocol should be secure against malicious acts; (c) no bidder can act for another bidder; (d) no one can know who else is bidding until the time comes for the bids to be opened; (e) no one can discover the contents of any of the bids until the time comes for the bids to be opened; (f) the successful bid must have been submitted before the bidding deadline; (g) all bidders can verify that the auction policy has been correctly implemented; (h) the successful bidder can be identified without being required to make himself or herself known; and (i) the bidding contents cannot be altered. The protocol consists of three subprotocols: the Registration Subprotocol, the Bidding Subprotocol, and the Auction Subprotocol. The protocol parameters and algorithm are described in detail.