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Standard quantum bit commitment - an indefinite commitment time.

Muhammad Nadeem

Published Jan 1, 2016• 0 citations

Abstract

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.

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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.

In a secure bit commitment protocol involving only classical physics, A commits either a

0

or a

1

to B. If quantum information is used in the protocol, A may be able to commit a state of the form $\ensuremath{\alpha}|0〉+\ensuremath{\beta}|1〉.$ If so, she can also commit mixed states in which the committed bit is entangled with other quantum states under her control. We introduce here a quantum cryptographic primitive, bit commitment with a certificate of classicality (BCCC), which differs from standard bit commitment in that it guarantees that the committed state has a fixed classical value. We show that no unconditionally secure BCCC protocol based on special relativity and quantum theory exists. We also propose complete definitions of security for quantum and relativistic bit commitment.

As a fundamental cryptographic primitive, bit commitment has lots of important and practical applications in modern cryptography. All previously proposed non-relativistic quantum bit commitment protocols cannot evade the Lo–Chau and Mayers attacks. Furthermore, relativistic quantum bit commitment protocols require rigorous spacetime constraints. In this paper, we present a simple, feasible but practically secure quantum bit commitment protocol without any spacetime constraint. The security of the proposed protocol is based on non-relativistic quantum mechanics, but it can resist all known attacks, including the Lo–Chau and Mayers attacks in practice.

Quantum physics allows for unconditionally secure communication between parties that trust each other. However, when the parties do not trust each other such as in the bit commitment scenario, quantum physics is not enough to guarantee security unless extra assumptions are made. Unconditionally secure bit commitment only becomes feasible when quantum physics is combined with relativistic causality constraints. Here we experimentally implement a quantum bit commitment protocol with relativistic constraints that offers unconditional security. The commitment is made through quantum measurements in two quantum key distribution systems in which the results are transmitted via free-space optical communication to two agents separated with more than 20 km. The security of the protocol relies on the properties of quantum information and relativity theory. In each run of the experiment, a bit is successfully committed with less than 5.68×10(-2) cheating probability. This demonstrates the experimental feasibility of quantum communication with relativistic constraints.

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.

We propose here a two-round relativistic bit commitment scheme where committer commits in the first round and then confirms his/her commitment in the second round. The scheme offers indefinite commitment time where both committer and receiver extract non-locally correlated measurement outcomes during the scheme that can be stored and revealed after arbitrarily long time. We show that the proposed scheme turns out to be a multiparty bit commitment scheme where both parties commit and reveal simultaneously. The multiparty generalization would have applications in business and secure multiparty computations such as managing joint bank account, holding joint shares in stock exchange and blind bidding. The same bit commitment scheme can also be used for the commitment of arbitrarily long classical bit strings. The scheme can be applied efficiently with existing technologies; entanglement is required only for time t=x/c where x is the special distance, can be as small as possible, between the committer and receiver.