Blockchain Based M+1st-Price Auction With Exponential Bid Upper Bound

Blockchain Based M+1st-Price Auction With Exponential Bid Upper Bound

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An auction is commonly used to sell limited resources in modern society.M+1st-price auction sells M identical goods to B bidders.The top M winners can buy the goods at the M+1st-price.

Each bidder sends their bids secretly as a bit-slice bidding vector to a trusted manager.Bit-slice is commonly used to compare secret values without revealing them.However, the bit-slice bidding vector also limits the upper bound of a bid as the length of the bidding vector.

A binary format Coffee Airpots bidding vector was proposed to increase the bid upper bound to an exponential scale.For example, given a bidding vector with length 32, a binary format bidding vector can increase the bid upper bound from 32 to two to the power Sunflower Seeds of 32.However, previous protocols that use binary format bidding vectors require a somewhat homomorphic encryption (SHE) and a trusted manager.

To make sure no party except the bidder itself knows its bid, our protocol does not have any managers.Instead, each bidder interacts with the Smart Contract independently.We propose a zero-knowledge proof that allows our protocol only requires partially homomorphic encryption such as an ElGamal encryption.

To our best knowledge, our protocol is the first secure M+1st-price auction protocol that can reach an exponential bid upper bound without a manager and SHE.