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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Secure bit commitment based on quantum one-way function

Bo Hao Yu, Zheng-Wei Zhou, Jian Li, Guang‐Can Guo

Published Sep 11, 2002• 2 citations

Abstract

Although Mayers, Lo and Chau successfully showed that unconditionally secure quantum bit commitment (QBC) is impossible, we present a secure QBC protocol which is quite different from the model used in their proofs. If Alice wants to commit a bit b, she first encodes b into a series of classical bit strings of the same length. The requirement is that the modulo 2 sum of all bits in every bit string equals to b. Then Alice uses quantum one-way function to produce quantum states which are corresponding to the encoded classical bit strings and will be sent to Bob as evidence. The quantum one-way function used here is just that was successfully applied in Gottesman and Chuang's quantum digital signatures. When it comes to the unveilingtime, Alice only sends the bit strings to Bob. Finally, Bob generates quantum states form the bit strings by the same quantum one-way function and uses controlled-swap circuit to check whether the quantum states are identical with the evidence.

DOI: 10.1117/12.483024

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Although Mayers, Lo and Chau successfully showed that unconditionally secure quantum bit commitment (QBC) is impossible, we present a secure QBC protocol which is quite different from the model used in their proofs. If Alice wants to commit a bit b, she first encodes b into a series of classical bit strings of the same length. The requirement is that the modulo 2 sum of all bits in every bit string equals to b. Then Alice uses quantum one-way function to produce quantum states which are corresponding to the encoded classical bit strings and will be sent to Bob as evidence. The quantum one-way function used here is just that was successfully applied in Gottesman and Chuang's quantum digital signatures. When it comes to the unveilingtime, Alice only sends the bit strings to Bob. Finally, Bob generates quantum states form the bit strings by the same quantum one-way function and uses controlled-swap circuit to check whether the quantum states are identical with the evidence.

Einstein-Podolsky-Rosen- (EPR) and the more powerful Mayers-Lo-Chau attack impose a serious constraint on quantum bit commitment (QBC). As a way to circumvent them, it is proposed that the quantum system encoding the commitment chosen by the committer (Alice) should be initially prepared in a seperable quantum state known to and furnished by the acceptor (Bob), rather than Alice. Classical communication is used to conclude the commitment phase and bind Alice's subsequent unveiling. Such a class of secure protocols can be built upon currently proposed QBC schemes impervious to a simple EPR attack. A specific scheme based on the Brassard-Crepeau-Josza-Langlois protocol is presented here as an example.

Quantum bit commitment has been known to be impossible by the independent proofs of Mayers, and Lo and Chau, even though several quantum bit commitment protocols have been proposed. However, we here point out that their proof is available only for one-way quantum bit commitment protocols, and present a simple and efficient quantum bit commitment protocol with two-way quantum communications. The unconditional security of our protocol is guaranteed by the additional unknownness and randomness generated by both users.

The existence of unconditionally secure quantum bit commitment (QBC) is excluded by the Mayers-Lo-Chau no-go theorem. Here we look for the second-best: a QBC protocol that can defeat certain quantum attacks. By breaking the knowledge symmetry between the participants with quantum algorithm, a QBC protocol is proposed and is proven to be secure against a major kind of coherent attacks---the dummy attack, in which the participant makes an empty promise instead of committing to a specific bit. Therefore it surpasses previous QBC protocols which are secure against individual attacks only.

Quantum bit commitment has been known to be impossible by the independent proofs of Mayers, and Lo and Chau, under the assumption that the whole quantum states right before the unveiling phase are static to users. We here provide an unconditionally secure non-static quantum bit commitment protocol with a trusted third party, which is not directly involved in any communications between users and can be limited not to get any information of commitment without being detected by users. We also prove that our quantum bit commitment protocol is not secure without the help of the trusted third party. The proof is basically different from the Mayers-Lo-Chau's no-go theorem, because we do not assume the staticity of the finally shared quantum states between users.

A semi-counterfactual quantum bit commitment (SCQBC) protocol is presented here for the first time, which makes use of counterfactual property. Similar to a counterfactual quantum key distribution scheme, half-photons are not transmitted through the quantum channel in our proposed protocol. In the SCQBC protocol, Bob, the verification party of the quantum bit commitment (QBC), sends the states while Alice, the commitment party, receives. Since Alice cannot receive all the states and entangle the commit bits with the verifier's registers, it is not subject to Mayers' and Lo-Chau's no-go theorem. In addition, a general bit commitment framework can be extracted from the SCQBC scheme, which opens up a new class of cryptographic protocols in counterfactual cryptography.

The desire to obtain an unconditionally secure bit commitment protocol in quantum cryptography was expressed for the first time thirteen years ago. Bit commitment is sufficient in quantum cryptography to realize a variety of applications with unconditional security. In 1993, a quantum bit commitment protocol was proposed together with a security proof. However, a basic flaw in the protocol was discovered by Mayers in 1995 and subsequently by Lo and Chau. Later the result was generalized by Mayers who showed that unconditionally secure bit commitment is impossible. A brief review on quantum bit commitment which focuses on the general impossibility theorem and on recent attempts to bypass this result is provided.