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arXiv:quant-ph/0207089

Quantum bit commitment and unconditional security

Horace P. Yuen

Published Jul 16, 2002• 4 citations
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Abstract

It is generally believed that unconditionally secure quantum bit commitment is impossible, due to widespread acceptance of an impossibility proof that utilizes quantum entaglement cheating. In this paper, we delineate how the impossibiliy proof formulation misses various types of quantum bit commitment protocols based on two-way quantum communications. We point out some of the gaps in the impossibility proof reasoning, and present corresponding counterexamples. Four different types of bit commitment protocols are constructed with several new protocol techniques. A specific Type 4 protocol is described and proved unconditionally secure. Security analysis of a Type 1 protocol and a Type 2 protocol are also sketched. The security of Type 3 protocols is as yet open. A development of quantum statistical decision theory and quantum games is needed to provie a complete security analysis of many such protocols.

DOI
10.48550/arxiv.quant-ph/0207089

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It is generally believed that unconditionally secure quantum bit commitment is impossible, due to widespread acceptance of an impossibility proof that utilizes quantum entaglement cheating. In this paper, we delineate how the impossibiliy proof formulation misses various types of quantum bit commitment protocols based on two-way quantum communications. We point out some of the gaps in the impossibility proof reasoning, and present corresponding counterexamples. Four different types of bit commitment protocols are constructed with several new protocol techniques. A specific Type 4 protocol is described and proved unconditionally secure. Security analysis of a Type 1 protocol and a Type 2 protocol are also sketched. The security of Type 3 protocols is as yet open. A development of quantum statistical decision theory and quantum games is needed to provie a complete security analysis of many such protocols.
The ``impossibility proof'' on unconditionally secure quantum bit commitment is critically analyzed. Many possibilities for obtaining a secure bit commitment protocol are indicated, purely on the basis of two-way quantum communications, which are not covered by the impossibility proof formulation. They are classified under six new types of protocols, with security proofs for specific examples on four types. Reasons for some previously failed attempts at obtaining secure protocols are also indicated.
Bit commitment involves the submission of evidence from one party to another so that the evidence can be used to confirm a later revealed bit value by the first party, while the second party cannot determine the bit value from the evidence alone. It is widely believed that secure quantum bit commitment is impossible due to quantum entanglement cheating, which is codified in a general impossibility theorem. In this paper, the scope of this general impossibility proof is extended and analyzed, and gaps are found. Three specific protocols are described for which the entanglement cheating as given in the impossibility proof fails to work. One of these protocols, QBC2, is proved to be unconditionally secure.
Bit commitment involves the submission of evidence from one party to another so that the evidence can be used to confirm a later revealed bit value by the first party, while the second party cannot determine the bit value from the evidence alone. It is widely believed that unconditionally secure quantum bit commitment is impossible due to quantum entanglement cheating, which is codified in a general impossibility theorem. In this paper, the scope of this general impossibility proof is analyzed, and gaps are found. Two variants of a bit commitment scheme utilizing anonymous quantum states and decoy states are presented. In the first variant, the exact verifying measurement is independent of the committed bit value, thus the second party can make it before the first party opens, making possible an unconditional security proof based on no-cloning. In the second variant, the impossibility proof fails because quantum entanglement purification of a mixed state does not render the protocol determinate. Whether impossibility holds in this or similar protocols is an open question, although preliminary results already show that the impossibility proof cannot work as it stands.
The commitment of bits between two mutually distrustful parties is a powerful cryptographic primitive with which many cryptographic objectives can be achieved. It is widely believed that unconditionally secure quantum bit commitment is impossible due to quantum entanglement cheating, which is codified in a general impossibility theorem. Gaps in the proof of this impossibility theorem are found. An unconditionally secure bit commitment protocol utilizing anonymous quantum states and the no-clone theorem is presented below with a full security proof.
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.