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arXiv:0801.0690

Quantum bit commitment protocol without quantum memory

Rubens Viana Ramos, Fábio Alencar Mendonça

Published Jan 4, 2008• 3 citations
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Abstract

Quantum protocols for bit commitment have been proposed and it is largely accepted that unconditionally secure quantum bit commitment is not possible; however, it can be more secure than classical bit commitment. In despite of its usefulness, quantum bit commitment protocols have not been experimentally implemented. The main reason is the fact that all proposed quantum bit commitment protocols require quantum memory. In this work, we show a quantum bit commitment protocol that does not require quantum memory and can be implemented with present technology.

DOI
10.48550/arxiv.0801.0690

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Quantum protocols for bit commitment have been proposed and it is largely accepted that unconditionally secure quantum bit commitment is not possible; however, it can be more secure than classical bit commitment. In despite of its usefulness, quantum bit commitment protocols have not been experimentally implemented. The main reason is the fact that all proposed quantum bit commitment protocols require quantum memory. In this work, we show a quantum bit commitment protocol that does not require quantum memory and can be implemented with present technology.
In classical cryptography, the bit commitment scheme is one of the most important primitives. We review the state of the art of bit commitment protocols, emphasizing its main achievements and applications. Next, we present a practical quantum bit commitment scheme, whose security relies on current technological limitations, such as the lack of long-term stable quantum memories. We demonstrate the feasibility of our practical quantum bit commitment protocol and that it can be securely implemented with nowadays technology.
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.
Zero-knowledge proof system is an important protocol that can be used as a basic block for construction of other more complex cryptographic protocols. Quantum zero-knowledge protocols have been proposed but, since their implementation requires advanced quantum technology devices, experimental implementation of zero-knowledge protocols have not being reported. In this work, we present a quantum zero-knowledge protocol based on a quantum bit commitment protocol that can be implemented with today technology. Hence, our quantum zero-knowledge protocol can be readily implemented.
Currently, it is believed in the literature that unconditionally secure bit commitment is impossible in non-relativistic quantum cryptography while only a weaker notion of bit commitment with finite commitment time is achievable in relativistic quantum setting. Moreover, relativistic classical bit commitment protocols allow arbitrary long commitment time but such protocols are not practically feasible; either because of multiple rounds of communication that result in exponential increase in communication complexity or due to asymptotic nature of security argument. The impossibility of practically feasible standard bit commitment leaves an obvious skepticism on the completeness of Hilbert space quantum cryptography and its claims of unconditional security. Contrary to the previously proposed results, we demonstrate here that an information-theoretic standard bit commitment scheme can be devised by using rules of purely non-relativistic quantum mechanics only; neither additional resources from theory of relativity nor multiple rounds of communications are required. The proposed bit commitment scheme can be applied efficiently with existing quantum technologies without long term quantum memory; quantum entanglement is required only for time t+δ where t is the communication time between the committer and receiver while δ << t is the processing time at laboratory.
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.
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.