Privacy-Preserving Comparable Commitment Scheme for Secure System
Hideaki Miyaji, Hiroshi Yamamoto · 2025
A commitment scheme is a cryptographic scheme that can verify the authenticity of the sender's input value. The verifiability of the input value is a main feature of commitment schemes suitable for sealed-bid auctions. The sealed-bid auction is a scheme of finding who is the highest bidder with the bidding price hidden. On the other hand, since the bidding value depends on the amount one can pay oneself, publishing the bidding value is as same act as publishing the amount of the user bank account. Galal and Youssef constructed a verifiable sealed-bid auction based on the homomorphic commitment scheme in 2018. In their scheme, the bidding price of the user is converted to a commitment value, and they used an interactive zero-knowledge proof to hide all users' input values in their scheme. However, their scheme uses zero-knowledge proof to guarantee the privacy-preserving. It is simpler to construct a scheme without using zero-knowledge proofs, and it is more efficient since the verification time is smaller. To overcome this problem, we propose the Privacy-Preserving Comparable Commitment Scheme (PPCCS) to identify who has the highest input value without using zero-knowledge proof. Our PPCCS uses a special encoding scheme called 0/1-Encoding to construct a commitment value, which allows Receiver (verifier) to identify who has the largest input value during the commitment phase. Moreover, our PPCCS is even more privacy-preserving than general homomorphic commitment schemes, since no other sender except Receiver can compare each commitment value. We also prove our PPCCS satisfies binding and hiding properties.