We consider a strategic problem of the Evesdropping to quantum key distribution. Evesdropper hopes to obtain the maxium information given the disturbance to the qubits is often For this strategy, the optimized individual attack have been extensively constructed under various conditions. However, it seems a difficult task in the case of coherent attack, i.e., Eve may treat a number of intercepted qubits collectively, including the collective unitary transformations and the measurements. It was conjectured by Cirac and Gisin that no coherent attack can be more powerful for this strategy for BB84 protocol. In this paper we give a general conclusion on the role of coherent attacks for the strategy of maxmizing the information given the disturbance. Suppose in a quantum key distribution(QKD) protocol, all the transmitted bits from Alice are independent and only the individual disturbances to each qubits are examined by Alice and Bob. For this type of protocols(so far almost all QKD protocols belong to this type), in principle no coherent attack is more powerful than the product of optimized individual attack to each individual qubits. All coherent attacks to the above QKD protocols can be disregarded for the strategy above.
We consider a strategic problem of the Evesdropping to quantum key distribution. Evesdropper hopes to obtain the maxium information given the disturbance to the qubits is often For this strategy, the optimized individual attack have been extensively constructed under various conditions. However, it seems a difficult task in the case of coherent attack, i.e., Eve may treat a number of intercepted qubits collectively, including the collective unitary transformations and the measurements. It was conjectured by Cirac and Gisin that no coherent attack can be more powerful for this strategy for BB84 protocol. In this paper we give a general conclusion on the role of coherent attacks for the strategy of maxmizing the information given the disturbance. Suppose in a quantum key distribution(QKD) protocol, all the transmitted bits from Alice are independent and only the individual disturbances to each qubits are examined by Alice and Bob. For this type of protocols(so far almost all QKD protocols belong to this type), in principle no coherent attack is more powerful than the product of optimized individual attack to each individual qubits. All coherent attacks to the above QKD protocols can be disregarded for the strategy above.
So far, the knowledge of Eve has been modeled by a classical random variable. The aim of this chapter is first to discuss how the previous results apply to QKD, where Eve's action may not necessarily be classically described by the random variable Z . Then, we explain the equivalence between BB84 and so-called entanglement purification protocols as a tool to encompass general eavesdropping strategies. Finally, we apply this equivalence to the case of the coherent-state protocol GG02. Eavesdropping strategies and secret-key distillation In Chapters 10 and 11, I analyzed the security of the protocols with regard to individual eavesdropping strategies only. In this particular case, the result of Alice's, Bob's and Eve's measurements can be described classically and the results of Section 6.4 apply. Let us review other kinds of eavesdropping strategies and discuss how the concepts of Chapter 6 can be applied. Note that the individual eavesdropping strategy, the simplest class of strategies, is still technologically very challenging to achieve today in an optimal way. Nevertheless, we do not want the security of quantum cryptography to rely only on technological barriers. By considering more general eavesdropping strategies, we make sure quantum cryptography lies on strong grounds. Following Gisin et al. [64], we divide the possible eavesdropping strategies into three categories: individual attacks, collective attacks and joint attacks .
In this paper, we discuss security of the six-state quantum key distribution protocol against intercept/resend attacks and collective attacks. For the intercept/resend attacks, we evaluate a probability that the legitimate users, Alice and Bob, do not notice interference caused by the eavesdropper Eve and a probability that Eve obtains a secret bit sent by Alice. For the collective attacks, we estimate not only the above two probabilities but also Eve's Shannon information. In the assessment of the security against the collective attacks, imposing looser constraints upon Eve's strategies than Bechmann-Pasquinucci and Gisin, we reach substantially the same result as their study. In other words, although we let Eve's strategies satisfy lower symmetry than Bechmann-Pasquinucci and Gisin, both their work and ours attain the same conclusion, i.e. the identical, unique, and optimum strategy. This implies that we obtain Eve's best tactic by applying simpler conditions to it than Bechmann-Pasquinucci and Gisin, so that this result is novel. Finally, we consider a relation between the six-state protocol and the E91 scheme. We show that the intercept/resend attacks can always be described by hidden variable models. In contrast, we demonstrate that we cannot regard the collective attacks as the hidden variable theories if the disturbance is smaller than 1/3.
Cryptanalysis is an important branch in the study of cryptography, including both the classical cryptography and the quantum one. In this paper we analyze the security of two three-party quantum key distribution protocols (QKDPs) proposed recently, and point out that they are susceptible to a simple and effective attack, i.e., the dense-coding attack. It is shown that the eavesdropper Eve can totally obtain the session key by sending entangled qubits as the fake signal to Alice and performing collective measurements after Alice's encoding. The attack process is just like a dense-coding communication between Eve and Alice, where a special measurement basis is employed. Furthermore, this attack does not introduce any errors to the transmitted information and consequently will not be discovered by Alice and Bob. The attack strategy is described in detail and a proof for its correctness is given. Finally, the root cause of this insecurity and a possible way to improve these protocols are discussed.
Cryptanalysis is an important branch in the study of cryptography, including both the classical cryptography and the quantum one. In this paper we analyze the security of two three-party quantum key distribution protocols (QKDPs) proposed recently, and point out that they are susceptible to a simple and effective attack, i.e. the dense-coding attack. It is shown that the eavesdropper Eve can totally obtain the session key by sending entangled qubits as the fake signal to Alice and performing collective measurements after Alice's encoding. The attack process is just like a dense-coding communication between Eve and Alice, where a special measurement basis is employed. Furthermore, this attack does not introduce any errors to the transmitted information and consequently will not be discovered by Alice and Bob. The attack strategy is described in detail and a proof for its correctness is given. At last, the root of this insecurity and a possible way to improve these protocols are discussed.
The information-disturbance tradeoff lies at the heart of quantum key distribution (QKD), allowing a sender and a receiver to monitor eavesdropping in the communication channel by checking for errors in the transmission. Even so, here we show that for a class of QKD protocols based on the principle of interaction-free measurement, an eavesdropper Eve can obtain partial information noiselessly, i.e., in such a way that the disturbance produced does not show up during the error checking. The proposed attack is shown to be the optimal individual noiseless attack. An implication of the noiselessness is that even though error correction is not required, privacy amplification (PA) is necessary. For example, in the case of the protocol of [T.-G. Noh, PRL 103, 230501 (2009)], the compression factor of PA is 0.68 in the case of an individual, noiseless attack. For the noisy generalization of the above attack, where Eve introduces noise into the communication channel without adding noise to the eavesdropping channel, the security requirement entails a lower bound on the noise threshold of about 11%, assuming that the transmitted particles are single photons.
Quantum cryptographic protocols are typically analyzed by assuming that potential opponents can carry out all physical operations, an assumption which grants capabilities far in excess of present technology. Adjusting this assumption to reflect more realistic capabilities is an attractive prospect, but one that can only be justified with a rigorous, quantitative framework that relates adversarial restrictions to the protocol's security and performance. We investigate the effect of limitations on the eavesdropper's (Eve's) ability to make a coherent attack on the security of continuous-variable quantum key distribution (CV-QKD). We consider a realistic attack in which the total decoherence induced during the attack is modeled by a Gaussian channel. Based on our decoherence model, we propose an optimal hybrid attack, which allows Eve to perform a combination of both coherent and individual attacks simultaneously. We evaluate the asymptotic and composable finite-size security of a heterodyne CV-QKD protocol against such hybrid attacks in terms of Eve's decoherence. We show that when the decoherence is greater than a threshold value, Eve's most effective strategy is reduced to the individual attack. Thus, if we are willing to assume that the decoherence caused by the memory and the collective measurement is large enough, it is sufficient to analyze the security of the protocol only against individual attacks, which significantly improves the CV-QKD performance in terms of both the key rate and maximum secure transmission distance.