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arXiv:1101.4620 · New Journal of Physics

Unconditionally secure bit commitment with flying qudits

Adrian Kent

Published Nov 11, 2011• 88 citations
arXivHTMLPDF

Abstract

In the task cryptographers call bit commitment, one party encrypts a prediction in a way that cannot be decrypted until they supply a key, but has only one valid key. Bit commitment has many applications, and has been much studied, but completely and provably secure schemes have remained elusive. Here we report a new development in physics-based cryptography which gives a completely new way of implementing bit commitment that is perfectly secure. The technique involves sending a quantum state (for instance one or more photons) at light speed in one of two or more directions, either along a secure channel or by quantum teleportation. Its security proof relies on the no-cloning theorem of quantum theory and the no-superluminal-signalling principle of special relativity.

DOI
10.1088/1367-2630/13/11/113015

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In the task cryptographers call bit commitment, one party encrypts a prediction in a way that cannot be decrypted until they supply a key, but has only one valid key. Bit commitment has many applications, and has been much studied, but completely and provably secure schemes have remained elusive. Here we report a new development in physics-based cryptography which gives a completely new way of implementing bit commitment that is perfectly secure. The technique involves sending a quantum state (for instance one or more photons) at light speed in one of two or more directions, either along a secure channel or by quantum teleportation. Its security proof relies on the no-cloning theorem of quantum theory and the no-superluminal-signalling principle of special relativity.
Bit commitment (BC) is an important cryptographic primitive for an agent to convince a mutually mistrustful party that she has already made a binding choice of 0 or 1 but only to reveal her choice at a later time. Ideally, a BC protocol should be simple, reliable, easy to implement using existing technologies, and most importantly unconditionally secure in the sense that its security is based on an information-theoretic proof rather than computational complexity assumption or the existence of a trustworthy arbitrator. Here we report such a provably secure scheme involving only one-way classical communications whose unconditional security is based on no superluminal signaling (NSS). Our scheme is inspired by the earlier works by Kent, who proposed two impractical relativistic protocols whose unconditional securities are yet to be established as well as several provably unconditionally secure protocols which rely on both quantum mechanics and NSS. Our scheme is conceptually simple and shows for the first time that quantum communication is not needed to achieve unconditional security for BC. Moreover, with purely classical communications, our scheme is practical and easy to implement with existing telecom technologies. This completes the cycle of study of unconditionally secure bit commitment based on known physical laws.
We propose a new unconditionally secure bit commitment scheme based on Minkowski causality and the properties of quantum information. The receiving party sends a number of randomly chosen Bennett-Brassard 1984 (BB84) qubits to the committer at a given point in space-time. The committer carries out measurements in one of the two BB84 bases, depending on the committed bit value, and transmits the outcomes securely at (or near) light speed in opposite directions to remote agents. These agents unveil the bit by returning the outcomes to adjacent agents of the receiver. The protocol's security relies only on simple properties of quantum information and the impossibility of superluminal signalling.
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 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.
We propose a new classical bit commitment protocol using the relativistic constraint that signals cannot travel faster than the speed of light ccc. This protocol is unconditionally secure against both classical or quantum attacks. The sender (Alice) and the receiver (Bob) each controls two secure stations separated by a large distance ddd, and they communicate by exchanging classical information only. Alice commits by sending from her stations two causally independent encrypted messages to the neighboring Bob's stations, after that the protocol is out of her control and she plays no role in the unveiling phase. The commitment remains concealed for a period of Δt=d/2cΔt=d/2cΔt=d/2c. This protocol requires only limited communication resources and is readily implementable with current technologies.
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.