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arXiv:0804.3531

Practically secure quantum bit commitment based on quantum seals

Guang Ping He, Z. D. Wang

Published Apr 22, 2008• 1 citation
arXivHTMLPDF

Abstract

The relationship between the quantum bit commitment (QBC) and quantum seal (QS) is studied. It is elaborated that QBC and QS are not equivalent, but QS protocols satisfying a stronger unconditional security requirement can lead to an unconditionally secure QBC. In this sense, QS is strictly stronger than QBC in security requirements. Based on an earlier proposal on sealing a single bit, a feasible QBC protocol is also put forward, which is secure in practice even if the cheater has a strong quantum computational power.

DOI
10.48550/arxiv.0804.3531

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The relationship between the quantum bit commitment (QBC) and quantum seal (QS) is studied. It is elaborated that QBC and QS are not equivalent, but QS protocols satisfying a stronger unconditional security requirement can lead to an unconditionally secure QBC. In this sense, QS is strictly stronger than QBC in security requirements. Based on an earlier proposal on sealing a single bit, a feasible QBC protocol is also put forward, which is secure in practice even if the cheater has a strong quantum computational power.
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.
It is generally believed that unconditionally secure quantum bit commitment (QBC) is proven impossible by a "no-go theorem". We point out that the theorem only establishes the existence of a cheating unitary transformation in any QBC scheme secure against the receiver, but this fact alone is not sufficient to rule out unconditionally secure QBC as a matter of principle, because there exists no proof that the cheating unitary transformation must be known to the cheater in all possible cases. In this work, we show how to circumvent the "no-go theorem" and prove that unconditionally secure QBC is in fact possible.
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.
The claim of quantum cryptography has always been that it can provide protocols that are unconditionally secure, that is, for which the security does not depend on any restriction on the time, space, or technology available to the cheaters. We show that this claim does not hold for any quantum bit commitment protocol. Since many cryptographic tasks use bit commitment as a basic primitive, this result implies a severe setback for quantum cryptography. The model used encompasses all reasonable implementations of quantum bit commitment protocols in which the participants have not met before, including those that make use of the theory of special relativity.
The Bit Commitment (BC) is an important basic agreement in cryptography . The concept was first proposed by the winner of the Turing Award in 1995 ManuelBlum. Bit commitment scheme can be used to build up zero knowledge proof, verified secret sharing, throwing coins etc agreement.Simultaneously and Oblivious Transfer together constitute the basis of secure multi-party computations. Both of them are hotspots in the field of information security. We investigated unconditional secure Quantum Bit Commitment (QBC) existence. And we constructed a new bit commitment model – double prover bit commitment. The Quantum Bit Commitment Protocol can be resistant to errors caused by noise.