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arXiv:quant-ph/0407174 · Physical Review A

Implementable quantum-bit-string commitment protocol

Toyohiro Tsurumaru

Published Jan 7, 2005• 6 citations
arXivHTMLPDF

Abstract

Quantum-bit-string commitment [A. Kent, Phys. Rev. Lett. 90, 237901 (2003)] (QBSC) is a variant of bit commitment (BC). In this paper, we propose a QBSC protocol that can be implemented using currently available technology and prove its security under the same security criteria as discussed by Kent. QBSC is a generalization of BC, but has slightly weaker requirements, and our proposed protocol is not intended to break the no-go theorem of quantum BC.

DOI
10.1103/physreva.71.012313

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Quantum-bit-string commitment [A. Kent, Phys. Rev. Lett. 90, 237901 (2003)] (QBSC) is a variant of bit commitment (BC). In this paper, we propose a QBSC protocol that can be implemented using currently available technology and prove its security under the same security criteria as discussed by Kent. QBSC is a generalization of BC, but has slightly weaker requirements, and our proposed protocol is not intended to break the no-go theorem of quantum BC.
Due to the high cost of the qubit generating device (QGD) (the single photon source), QGD may not be available at the same time in both communicating parties (Alice and Bob) who have to execute the quantum bit string commitment (QBSC) protocol for some application environments. All the existing QBSC protocols allow one-way commitment i.e., only the party (Bob) who possesses the QGD is allowed to commit a bit string to Alice who does not have the QGD, but not the other way around. However, what happens if Alice, who does not have the QGD, is required to commit a bit string to Bob? The current QBSC protocols fail to provide a solution in this case. Therefore, the purpose of this paper is to allow Alice, who is not equipped with the QGD, to commit a bit string to Bob who has the QGD. With our proposed protocol, together with previously proposed QBSC protocols, Alice and Bob can perform two-way commitment, even though Bob is the only party who is equipped with the QGD.
Several kinds of qubit-string-based(QS-based) bit commitment protocols are presented, and a definition of information-theoretic concealing is given. All the protocols presented here are proved to be secure under this definition. We suggest an attack algorithm to obtain the local unitary transformation introduced in no-go theorem, which is used to attack the binding condition, then study the security of our QS-based bit commitment protocols under this attack via introducing a new concept "physical security of protocol". At last we present a practical QS-based bit commitment scheme against channel loss and error.
A bit string commitment protocol securely commits N classical bits so that the recipient can extract only M<N bits of information about the string. Classical reasoning suggests that bit string commitment implies bit commitment and hence, given the Mayers-Lo-Chau theorem, that nonrelativistic quantum bit string commitment is impossible. Not so: there exist nonrelativistic quantum bit string commitment protocols, with security parameters epsilon and M, that allow A to commit N=N(M,epsilon) bits to B so that A's probability of successfully cheating when revealing any bit and B's probability of extracting more than N'=N-M bits of information about the N bit string before revelation are both less than epsilon. With a restrictive definition of security against A, N can be taken to be O(exp(CN')) for a positive constant C. I briefly discuss possible applications.
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.