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Physical Review A

In quantum direct communication an undetectable eavesdropper can always tell Ψ from Φ Bell states in the message mode

Mladen Pavičić

Published Apr 22, 2013• 17 citations
Publisher

Abstract

We show that in any quantum direct communication protocol that is based on $\ensuremath{\Psi}$ and $\ensuremath{\Phi}$ Bell states, an eavesdropper can always tell $\ensuremath{\Psi}$ from $\ensuremath{\Phi}$ states without altering the transmission in any way in the message mode. This renders all protocols that make use of only one $\ensuremath{\Psi}$ state and one $\ensuremath{\Phi}$ state completely insecure in the message mode. All four-Bell-state protocols require a revision and this might be of importance for new implementations of entanglement-based cryptographic protocols. The detection rate of an eavesdropper is 25$%$ per control transmission, i.e., a half of the rate in the two-state (ping-pong) protocol. An eavesdropper can detect control probes with certainty in the standard control transmission without a photon in the Alice-to-Bob's travel mode and with near certainty in a transmission with a fake photon in the travel mode. Resending of measured control photons via the travel mode would make an eavesdropper completely invisible.

DOI
10.1103/physreva.87.042326

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We show that in any quantum direct communication protocol that is based on \ensuremathΨ\ensuremath{\Psi}\ensuremathΨ and \ensuremathΦ\ensuremath{\Phi}\ensuremathΦ Bell states, an eavesdropper can always tell \ensuremathΨ\ensuremath{\Psi}\ensuremathΨ from \ensuremathΦ\ensuremath{\Phi}\ensuremathΦ states without altering the transmission in any way in the message mode. This renders all protocols that make use of only one \ensuremathΨ\ensuremath{\Psi}\ensuremathΨ state and one \ensuremathΦ\ensuremath{\Phi}\ensuremathΦ state completely insecure in the message mode. All four-Bell-state protocols require a revision and this might be of importance for new implementations of entanglement-based cryptographic protocols. The detection rate of an eavesdropper is 25% per control transmission, i.e., a half of the rate in the two-state (ping-pong) protocol. An eavesdropper can detect control probes with certainty in the standard control transmission without a photon in the Alice-to-Bob's travel mode and with near certainty in a transmission with a fake photon in the travel mode. Resending of measured control photons via the travel mode would make an eavesdropper completely invisible.
We introduce an attack scheme for eavesdropping freely the ping-pong quantum communication protocol proposed by Boström and Felbinger [ Phys. Rev. Lett. 89 , 187902 (2002)] in a noise channel. The vicious eavesdropper, Eve, intercepts and measures the travel photon transmitted between the sender and the receiver. Then she replaces the quantum signal with a multi-photon signal in the same state, and measures the returned photons with the measuring basis, with which Eve prepares the fake signal except for one photon. This attack increases neither the quantum channel losses nor the error rate in the sampling instances for eavesdropping check. It works for eavesdropping the secret message transmitted with the ping-pong protocol. Finally, we propose a way for improving the security of the ping-pong protocol.
Ping-Pong protocol is a Quantum Secure Direct Communication protocol that fails to transfer a secure key or secret message optimally in a lossy or noisy channel. The reason is an eavesdropper who possibly hides in the light of these channel losses and gains information about the secure key bits or secret messages. We propose an efficient modification to the control mode of the original Ping-Pong protocol leading to the detection of an eavesdropper with a much higher probability which may not allow her to hide in the light of lossy channels. Assuming that Eve knows and makes a fixed number of right guesses about the modification in the protocol, an optimum ratio of modification can be evaluated. In addition, it is shown that incorporation of the proposed modification in the protocol doubles the eavesdropper’s detection probability for certain eavesdropping operations.
A controlled bidirectional quantum secure direct communication protocol without information leakage was proposed.In the proposed protocol,two authenticated communication parties,Alice and Bob,were able to securely exchange their secret messages simultaneously under the control of the controller,Charlie.The problem of information leakage was overcome by making full use of the measurement correlation property after entanglement swapping among three Bell states.Moreover,the proposed protocol merely took the Bell state as quantum resource and merely needed the Bell measurement so that it was convenient to implement.Security analysis shows that the proposed protocol can detect not only the active attacks from the outside eavesdropper,but also the dishonest behavior from the controller,Charlie.It can be concluded that the proposed protocol has good security.
A quantum circuit providing an undetectable eavesdropping of information in message mode, which compromises all two-state [Formula: see text]-[Formula: see text] quantum direct communication (QDC) protocols, has been recently proposed by Pavičić [Phys. Rev. A 87 (2013) 042326]. A modification of the protocol’s control mode is proposed, which improves users’ 25% detection probability of Eve to 50% at best, as that in ping-pong protocol. The modification also improves the detection probability of Wójcik’s attack [Phys. Rev. Lett 90 (2003) 157901] to 75% at best. The resistance against man-in-the-middle (MITM) attack as well as the discussion of security for four Bell state protocols is presented. As a result, the protocol security is strengthened both theoretically and practically, and quantum advantage of superdense coding is restored.
We consider a man-in-the-middle attack on two-way quantum key distribution ping-pong and LM05 protocols in which an eavesdropper copies all messages in the message mode, while being undetectable in the mode. Under the attack there is therefore no disturbance in the message mode and the mutual information between the sender and the receiver is always constant and equal to one and messages copied by the eavesdropper are always genuine. An attack can only be detected in the control mode but the level of detection at which the protocol should be aborted is not defined. We examine steps of the protocol to evaluate its security and find that the protocol should be redesigned. We also compare it with the security of a one-way asymmetric BB84-like protocol in which one basis serves as the message mode and the other as the control mode but which does have the level of detection at which the protocol should be aborted defined.
The quantum secure direct communication is a new-style quantum communication scheme. It arouses much interest recently. The ping-pong protocol proposed by Bostroem and Felbinger is one of relatively mature quantum secure direct communication protocols, which is asymptotically secure under Eve's eavesdropping attack. But it ignores the message authentication. Being aimed at this problem, we propose a novel ping-pong protocol with authentication. The former has two operation modes, or the message mode and the control mode, which are used to send message and detect Eve's attack, respectively. But it just detects Eve's eavesdropping attack and does not authenticate the sent message in the control mode. The latter has also the above two operation modes, which employs a braid-based key agreement protocol for both the parties participating in communication to share a secret, whose size and magnitude are undecided in advance. Using the shared secret, it not only detects Eve's eavesdropping attack, but also effectively performs the message authentication in the control mode. It is also asymptotically secure under Eve's eavesdropping attack. The security of the proposed protocol is based on the no-cloning theorem, the correlations of quantum entanglement and the fact that the p-th root finding problem on braid groups is intractable even on quantum computers, as well as classical computers. In addition different from the original ping-pong protocol, the communication was initiated by the sender Alice instead of by the receiver Bob. This corresponds to the way of common communications. The present protocol not only can resist the attacks known recently, but should be experimentally feasible using today's technology.