Evaluating the theoretical limit of the amount of information Eve can steal from a quantum key distribution protocol under given conditions is one of the most important things that need to be done in security proof. In addition to source loopholes and detection loopholes, channel attacks are considered to be the main ways of information leakage, while collective attacks are considered to be the most powerful active channel attacks. Here we deduce in detail the capability limit of Eve's collective attack in non-entangled quantum key distribution, like BB84 and measurement-device-independent protocols, and entangled quantum key distribution, like device-independent protocol, in which collective attack is composed of quantum weak measurement and quantum unambiguous state discrimination detection. The theoretical results show that collective attacks are equivalent in entangled and non-entangled quantum key distribution protocols. We also find that compared with the security proof based on entanglement purification, the security proof based on collective attack not only improves the system's tolerable bit error rate, but also improves the key rate.
Evaluating the theoretical limit of the amount of information Eve can steal from a quantum key distribution protocol under given conditions is one of the most important things that need to be done in security proof. In addition to source loopholes and detection loopholes, channel attacks are considered to be the main ways of information leakage, while collective attacks are considered to be the most powerful active channel attacks. Here we deduce in detail the capability limit of Eve's collective attack in non-entangled quantum key distribution, like BB84 and measurement-device-independent protocols, and entangled quantum key distribution, like device-independent protocol, in which collective attack is composed of quantum weak measurement and quantum unambiguous state discrimination detection. The theoretical results show that collective attacks are equivalent in entangled and non-entangled quantum key distribution protocols. We also find that compared with the security proof based on entanglement purification, the security proof based on collective attack not only improves the system's tolerable bit error rate, but also improves the key rate.
The Quantum Key Distribution (QKD) protocol BB84 has been proven secure against several important types of attacks: the collective attacks and the joint attacks. Here we analyze the security of a modified BB84 protocol, for which information is sent only in the z basis while testing is done in both the z and the x bases, against collective attacks. The proof follows the framework of a previous paper (Boyer, Gelles, and Mor, 2009), but it avoids the classical information-theoretical analysis that caused problems with composability. We show that this modified BB84 protocol is as secure against collective attacks as the original BB84 protocol, and that it requires more bits for testing.
The security analysis of the Ekert 1991 (E91), Bennett 1992 (B92), six-state protocol, Scarani–Acín–Ribordy–Gisin 2004 (SARG04) quantum key distribution (QKD) protocols, and their variants have been studied in the presence of collective-rotation noise channels. However, besides the Bennett–Brassard 1984 (BB84) being the first proposed, extensively studied, and essential protocol, its security proof under collective-rotation noise is still missing. Thus, we aim to close this gap in the literature. Consequently, we investigate how collective-rotation noise channels affect the security of the BB84 protocol. Mainly, we study scenarios where the eavesdropper, Eve, conducts an intercept-resend attack on the transmitted photons sent via a quantum communication channel shared by Alice and Bob. Notably, we distinguish the impact of collective-rotation noise and that of the eavesdropper. To achieve this, we provide rigorous, yet straightforward numerical calculations. First, we derive a model for the collective-rotation noise for the BB84 protocol and parametrize the mutual information shared between Alice and Eve. This is followed by deriving the quantum bit error rate (QBER) for two intercept-resend attack scenarios. In particular, we demonstrate that, for small rotation angles, one can extract a secure secret key under a collective-rotation noise channel when there is no eavesdropping. We observe that noise induced by rotation of 0.35 radians of the prepared quantum state results in a QBER of 11%, which corresponds to the lower bound on the tolerable error rate for the BB84 QKD protocol against general attacks. Moreover, a rotational angle of 0.53 radians yields a 25% QBER, which corresponds to the error rate bound due to the intercept-resend attack. Finally, we conclude that the BB84 protocol is robust against intercept-resend attacks on collective-rotation noise channels when the rotation angle is varied arbitrarily within particular bounds.
Although some ideal quantum key distribution protocols have been proved to be secure, there have been some demonstrations that practical quantum key distribution implementations were hacked due to some real-life imperfections. Among these attacks, detector side channel attacks may be the most serious. Recently, a measurement device independent quantum key distribution protocol [ Phys. Rev. Lett. 108 (2012) 130503 ] was proposed and all detector side channel attacks are removed in this scheme. Here a new security proof based on quantum information theory is given. The eavesdropper's information of the sifted key bits is bounded. Then with this bound, the final secure key bit rate can be obtained.
Most of quantum cryptography protocols are designed under the ideal conditions without considering the impact of noise in actual communication; thus they may result in that the confidential information cannot be transmitted to the receiver accurately or eavesdroppers can steal the confidential information by mixing in noise. Therefore, analyzing the security of quantum cryptography protocols under noise conditions is of great significance. For the purpose of analyzing the security of quantum BB84 protocol in collective-rotation noise, firstly this paper introduces the quantum BB84 protocol, and considers the influence of environmental noise on it. An explanation should be stated that in a noise environment, the effects of noise and eavesdropping cannot be distinguished between each other. So the mechanism for which the error bit is simply used as the criterion to judge whether there exists eavesdropping in the BB84 protocol, cannot be used in the noise environment. The mechanism to judge whether there exists eavesdropping in quantum noise channel needs to be modified and improved for protecting the information. An initial qubit error rate can be set according to the noisy quantum channel. If the qubit error rate of the quantum communication channel is larger than that, it can be determined that the quantum channel is not secure and exists eavesdropping, no matter what the reason is. And on this basis, the collective-rotation noise model will be established in quantum channel by using the particle deflection model and distinguish the noise from the eavesdropping in quantum channel quantitatively, and the relationship of the amount of information that eavesdroppers can steal, the quantum bits error rate and the noise level will be analyzed by using the von Neumann entropy. Finally, the noise critical point will be calculated by using the collective noise model and the relationship between the amount of information that eavesdroppers can steal, at the quantum bits error rate, and the noise level. Through the analysis, we can know that in the existing noise level, the most of the eavesdropping can steal 25% of the key from the communication. However, the Eve's eavesdropping behavior will be detected, so that Alice and Bob will give up the current consultation key, and restart the key negotiation. This result shows that the quantum BB84 protocol is safe and secure in the collective-rotation noise channel. The research results of this paper will enrich the theory of quantum cryptography, and the innovation of security detection methods in quantum cryptographic protocols will help promote the process of practical quantum cryptography.
Practical quantum key distribution (QKD) systems operate under noise, but security of most protocols have been analyzed under ideal noiseless scenarios. In this work, we investigated security performance of BB84 protocol under effect of collective rotation noise. Using theoretical quantum information frameworks, we analyzed key security parameters including quantum bit error rate (QBER), mutual information and secret key rate (SKR). Security of protocol is studied under various eavesdropping scenarios based on intercept and resend attacks. Our results show that collective rotation noise has a significant impact on the information shared between the two parties. Particularly, we extended prior treatments by suggesting a noise engineering strategy where we identified a non-zero noise range where information accessed by Eve is minimized while corresponding SKR degradation remains relatively small. This analysis provide insights into robustness of BB84 protocol under realistic noisy channels and may contribute towards development of more resilient QKD systems.
The goal of quantum key distribution (QKD) is to establish a secure key between two parties connected by an insecure quantum channel. To use a QKD protocol in practice, one has to prove that a finite size key is secure against general attacks: no matter the adversary's attack, they cannot gain useful information about the key. A much simpler task is to prove security against collective attacks, where the adversary is assumed to behave identically and independently in each round. In this work, we provide a formal framework for general QKD protocols and show that for any protocol that can be expressed in this framework, security against general attacks reduces to security against collective attacks, which in turn reduces to a numerical computation. Our proof relies on a recently developed information-theoretic tool called generalised entropy accumulation and can handle generic prepare-and-measure protocols directly without switching to an entanglement-based version.