Improved Construnctions of Quantum Bit-Commitment Based on Quantum One-Way Permutations

A bit-commitment protocol involves two party: a sender (say Alice) and a receiver (say Bob). Alice has a classical string in mind, which she wants to communicate to Bob at a later time. In order to guarantee that she will not change her mind in the interim, Alice agrees to lock her commitment in a safe which she sends to Bob, but keeps the key of the safe. At the moment of truth, Alice unveils her commitment and opens the safe to prove her honesty. A bit-commitment protocol has two security requirements. One is binding that Alice cannot change her initial commitment without being detected. The other is concealing that Bob has no reasonable way of obtaining any information on Alice’s commitment before she discloses it. Since Bennett and Brassard [1] proposed the quantum key-exchange protocol, various quantum cryptographic protocols including bit-commitment have been investigated. However, Mayers [8] proved that any quantum bit-commitment scheme can either be defeated by Alice or Bob as long as both have unrestricted quantum computational power.