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arXiv:1011.5099

Qubit-string-based bit commitment protocols with physical security

Li Yang, Chong Xiang, Bao Li

Published Nov 23, 2010• 13 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.1011.5099

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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.
Bit commitment is an essential primitive in quantum cryptography. It is the basic building block of many cryptographic protocols in which it provides security over distrustful parties. This paper proposes a secured quantum two-bit commitment protocol for any two classical bits. The protocol contains two parties - a committer and a receiver - who share both quantum and classical communication channels. The main phases of this protocol are commitment and revealing phases where the concealing and binding conditions are proved in order to accept the commitment message. The proposed framework utilizes different security layers to hide specific quantum states in a superposition alongside trivial one qubit operations. The secured unitary transformations are applied by the two parties to meet the concealing and binding conditions. To verify the success of the proposed protocol, the measured output of the two parties are compared. The protocol operates under the assumption that the two parties might cheat and the possible existence of an eavesdropper.
We propose a framework of bit commitment protocol using a comparison scheme and present a compound comparison scheme based on counterfactual cryptography. Finally, we propose a counterfactual quantum bit commitment protocol. In security analysis, we give the proper security parameters for counterfactual quantum bit commitment and prove that intercept attack and intercept/resend attack are ineffective attack for our protocol. In addition, we explain that counterfactual quantum bit commitment protocol cannot be attacked with no-go theorem attack by current technology.
In quantum bit commitment(QBC),most existed proposals analyze little of communicating an innocent message over noisy quantum channels.These methods are not practical.Based on the information hiding characteristics of quantum steganography,a novel QBC protocal is proposed.An elegant scheme is presented for disguising secret information as quantum noise,and embedding it in stego qubits which encode into a codeword of quantum error-correcting code.The method is proved secure and effective in the presence of noisy quantum channel and it's a potential eavesdropper.The results of theoretical analysis and numerical simulation show that the proposed scheme has perfect concealing and binding properties. Theoretical analysis proved the validity.The method forms a theoretical basis for the promotion and application of quantum cryptographic protocols.
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.