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arXiv:quant-ph/0012075 · Journal of Experimental and Theoretical Physics

Relativistic quantum protocols: Bit commitment and coin tossing

S. N. Molotkov, S. S. Nazin

Published Oct 1, 2001• 0 citations
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Abstract

New relativistic quantum protocols realizing the bit commitment and coin tossing schemes are proposed. The protocols are based on the idea that spatially extended nonstationary orthogonal quantum states inaccessible for measurement cannot be unambiguously distinguished. As the states are transmitted from the region controlled by one party to the region accessible for measurement by the other party, the states become reliably distinguishable when accessed as a whole. Essential points of the protocol are both the quantum character of states and the existence of an ultimate signal propagation speed dictated by special relativity.

DOI
10.1134/1.1420458

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New relativistic quantum protocols realizing the bit commitment and coin tossing schemes are proposed. The protocols are based on the idea that spatially extended nonstationary orthogonal quantum states inaccessible for measurement cannot be unambiguously distinguished. As the states are transmitted from the region controlled by one party to the region accessible for measurement by the other party, the states become reliably distinguishable when accessed as a whole. Essential points of the protocol are both the quantum character of states and the existence of an ultimate signal propagation speed dictated by special relativity.
The relativistic quantum protocols realizing the bit commitment and distant coin tossing schemes are proposed. The protocols are based on the fact that the non-stationary orthogonal extended quantum states cannot be reliably distinguished if they are not fully accessible for the measurement. As the states propagate from the domain controlled by one of the user to the domain accessible for the measurements performed by the other user, they become reliably distinguishable for the second user. Important for the protocol are both the quantum nature of the states and the existence of a finite maximum speed of the signal propagation imposed by the special relativity. PACS numbers: 89.70.+c, 03.65.-w 1
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.
There had been well known claims of ``provably unbreakable'' quantum protocols for bit commitment and coin tossing. However, we, and independently Mayers, showed that all proposed quantum bit commitment (and therefore coin tossing) schemes are, in principle, insecure because the sender, Alice, can always cheat successfully by using an EPR-type of attack and delaying her measurements. One might wonder if secure quantum bit commitment and coin tossing protocols exist at all. Here we prove that an EPR-type of attack by Alice will, in principle, break {\em any} realistic quantum bit commitment and {\em ideal} coin tossing scheme. Therefore, provided that Alice has a quantum computer and is capable of storing quantum signals for an arbitrary length of time, all those schemes are insecure. Since bit commitment and coin tossing are useful primitives for building up more sophisticated protocols such as zero-knowledge proofs, our results cast very serious doubt on the security of quantum cryptography in the so-called ``post-cold-war'' applications.