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arXiv:1504.00944 · Physical Review A

Device-independent relativistic quantum bit commitment

Emily Adlam, Adrian Kent

Published Aug 7, 2015• 39 citations
arXivHTMLPDF

Abstract

We examine the possibility of device-independent relativistic quantum bit commitment, introducing three relativistic quantum bit commitment schemes that offer device-independent security against hypothetical postquantum adversaries subject only to the no-signaling principle. We discuss the potential threat of location attacks, in which the behavior of untrusted devices used in relativistic quantum cryptography depends on their space-time location and show that our protocols are secure against both location attacks and memory attacks. The protocols are compared to a relativistic classical bit commitment scheme with similar features and we note some advantages for the quantum schemes.

DOI
10.1103/physreva.92.022315

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We examine the possibility of device-independent relativistic quantum bit commitment, introducing three relativistic quantum bit commitment schemes that offer device-independent security against hypothetical postquantum adversaries subject only to the no-signaling principle. We discuss the potential threat of location attacks, in which the behavior of untrusted devices used in relativistic quantum cryptography depends on their space-time location and show that our protocols are secure against both location attacks and memory attacks. The protocols are compared to a relativistic classical bit commitment scheme with similar features and we note some advantages for the quantum schemes.
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.
Bit commitment is a fundamental cryptographic primitive in which Alice wishes to commit a secret bit to Bob. Perfectly secure bit commitment between two mistrustful parties is impossible through an asynchronous exchange of quantum information. Perfect security is, however, possible when Alice and Bob each split into several agents exchanging classical information at times and locations suitably chosen to satisfy specific relativistic constraints. In this Letter we first revisit a previously proposed scheme [C. Crépeau et al., Lect. Notes Comput. Sci. 7073, 407 (2011)] that realizes bit commitment using only classical communication. We prove that the protocol is secure against quantum adversaries for a duration limited by the light-speed communication time between the locations of the agents. We then propose a novel multiround scheme based on finite-field arithmetic that extends the commitment time beyond this limit, and we prove its security against classical attacks. Finally, we present an implementation of these protocols using dedicated hardware and we demonstrate a 2 ms-long bit commitment over a distance of 131 km. By positioning the agents on antipodal points on the surface of Earth, the commitment time could possibly be extended to 212 ms.
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.
A relativistic quantum exchange protocol making it possible to implement a bit commitment scheme is realized. The protocol is based on the idea that in the relativistic case the propagation of a field into a region of space accessible for measurement requires, in contrast to the nonrelativistic case, a finite time that depends on the structure of the states. The protocol requires one classical and several quantum communication channels. It turns out that it is possible in principle to preserve the secret bit for as long a period of time desired and with probability as close to 1 as desired.
If mistrustful parties A and B control two or more appropriately located sites, special relativity can be used to guarantee that a pair of messages exchanged by A and B are independent. Using this fact, an unconditionally secure relativistic bit commitment protocol, RBC1, was recently defined. Security is maintained in RBC1 by exchanging a sequence of messages whose transmission rate increases exponentially in time. We define here a variant, RBC2, which requires a constant transmission rate and can in practice be securely maintained for long periods. We also introduce a zero-knowledge proof protocol which allows A to convince B of the value of any function of NNN relativistic bit commitments without giving any further information. Applying this to the XOR of two bit commitments made by RBC1 or RBC2, we define two further relativistic bit commitment protocols, RBC3 and RBC4. These two protocols are permanently unconditionally secure against classical attack and require only a constant transmission rate. We conjecture that they are also unconditionally secure against quantum attack.