Abstract The decoy state method has been proposed to detect a photon number splitting (PNS) attack. Today, the decoy state method is considered to be an almost universal method for proving the secrecy of quantum cryptography protocols and calculating the length of a secret key. In this paper, it is shown that there exist attacks, for example, a beam splitting (BS) attack, to which the decoy state method turns out to be insensitive. The decoy state method is oriented to the detection of changes in the photocount statistics of information states and decoy states under a PNS attack. Under a BS attack, the photocount statistics is not changed. As a result, the decoy state method significantly overestimates the length of the key. Thus, the decoy state method is not a universal method that allows the detection of various attacks. Apparently, due to a large number of publications on the decoy state method, a widespread opinion has been formed that this method is universal. This fact has led to attempts to adopt this method as an international standard in quantum cryptography, which is clearly premature.
Abstract The decoy state method has been proposed to detect a photon number splitting (PNS) attack. Today, the decoy state method is considered to be an almost universal method for proving the secrecy of quantum cryptography protocols and calculating the length of a secret key. In this paper, it is shown that there exist attacks, for example, a beam splitting (BS) attack, to which the decoy state method turns out to be insensitive. The decoy state method is oriented to the detection of changes in the photocount statistics of information states and decoy states under a PNS attack. Under a BS attack, the photocount statistics is not changed. As a result, the decoy state method significantly overestimates the length of the key. Thus, the decoy state method is not a universal method that allows the detection of various attacks. Apparently, due to a large number of publications on the decoy state method, a widespread opinion has been formed that this method is universal. This fact has led to attempts to adopt this method as an international standard in quantum cryptography, which is clearly premature.
The existing decoy-state quantum key distribution (QKD) beating photon-number-splitting (PNS) attack provides a more accurate method to estimate the secure key rate, while it still considers that only single-photon pulses can generate secure keys in any case. However, multiphoton pulses can also generate secure keys if we can detect the possibility of PNS attack in the channel. The ultimate goal of this line of research is to confirm the absence of all types of PNS attacks. In particular, the PNS attack mentioned and detected in this paper is only the weaker version of PNS attack which significantly changes the observed values of the legitimate users. In this paper, under the null hypothesis of no weaker version of PNS attack, we first determine whether there is an attack or not by retrieving the missing information of the existing decoy-state protocols, extract a Cauchy distribution statistic, and further provide a detection method and the type I error probability. If the result is judged to be an attack, we can use the existing decoy-state method and the GLLP formula to estimate the secure key rate. Otherwise, the pulses with the same basis received including both single-photon pulses and multiphoton pulses, can be used to generate the keys and we give the secure key rate in this case. Finally, the associated experiments we performed (i.e., the significance level is 5%) show the correctness of our method.
With the potential of quantum computers to compromise current public-key cryptosystems, Quantum Key Distribution (QKD), which is based on the physical laws of quantum mechanics, has garnered significant attention. However, while QKD security proofs typically assume ideal single-photon sources, realistic implementations rely on Weak Coherent Pulses (WCP) due to the difficulties associated with commercializing true single-photon sources. Unfortunately, the multi-photon components inherent in WCPs are vulnerable to Photon Number Splitting (PNS) attacks, which limits the secure transmission distance to a few tens of kilometers. This article introduces the Decoy State method, which effectively resolves this issue. Proposed by W.-Y. Hwang in 2003 and further advanced by H.-K. Lo and X.-B. Wang, this technique utilizes the random interleaving of pulses with different mean photon numbers during transmission. By doing so, it enables the accurate estimation of single-photon yield and error rates, thereby effectively detecting PNS attacks. Because it can be implemented using standard commercial lasers and intensity modulators, the Decoy State method has become the standard technology in most modern QKD systems. It serves as a core component for long-distance quantum communication, enabling major milestones reported recently. This article reviews the principles, mathematical analysis, and latest applications of the Decoy State method.
Abstract We discuss the photon number splitting attack (PNS) in systems of quantum cryptography with phase coding. It is shown that this attack, as well as the structural equations for the PNS attack for phase encoding, differs physically from the analogous attack applied to the polarization coding. As far as we know, in practice, in all works to date processing of experimental data has been done for phase coding, but using formulas for polarization coding. This can lead to inadequate results for the length of the secret key. These calculations are important for the correct interpretation of the results, especially if it concerns the criterion of secrecy in quantum cryptography.
A new attack on the quantum key distribution is proposed involving joint collective unambiguous measurements of reflected probe states from an intensity modulator and photon number splitting (PNS) measurements, i.e., nondestructive measurements of the number of information photons in the quantum communication channel. This attack does not change the relative statistics of photocounts of states with different numbers of photons, does not lead to errors on the receiver side, and, thereby, is not detected by any of known methods, including the modified decoy state method. The attack results only in additional losses in the communication channel, which are not “controlled” by the decoy state method. The dependence of introduced losses on the intensity of reflected probe states is estimated. The critical level of losses depends on a particular physical implementation of the quantum cryptography system, which determines the upper bound of the intensity of reflected probe states. The knowledge of this bound is fundamentally necessary to ensure the security of keys. The fact that the attack does not lead to errors on the receiver side and does not change the relative statistics of photocounts but only results in additional losses, which depend on the intensity according to the distinguishability of reflected probe states, does not mean that this attack transforms quantum cryptography systems from the type of cryptographic systems where the security of keys is guaranteed by fundamental quantum mechanical laws to the type of systems where this security is guaranteed by technical restrictions. Even in the presence of side channels of information leakage, the security of keys is still guaranteed by fundamental quantum mechanical restrictions on the distinguishability of states. A low level of distinguishability (“intensity”) of quantum states in side channels is naturally reached by technical tools.
Abstract Quantum cryptography or, more precisely, quantum key distribution (QKD), is one of the advanced areas in the field of quantum technologies. The confidentiality of keys distributed with the use of QKD protocols is guaranteed by the fundamental laws of quantum mechanics. This paper is devoted to the decoy state method, a countermeasure against vulnerabilities caused by the use of coherent states of light for QKD protocols whose security is proved under the assumption of single-photon states. We give a formal security proof of the decoy state method against all possible attacks. We compare two widely known attacks on multiphoton pulses: photon-number splitting and beam splitting. Finally, we discuss the equivalence of polarization and phase coding.
Secure quantum key distribution (QKD) promises a revolutionizing in optical applications such as encryption, and imaging. However, their implementation in real-world scenarios continues to be challenged. The goal of this work is to verify the presence of photon number splitting (PNS) attack in quantum cryptography system based on BB84 protocol and to obtain a maximum secure key length as possible. This was realized through randomly interleaving decoy states with mean photon numbers of 5.38, 1.588, and 0.48 between the signal states with mean photon numbers of 2.69, 0.794, and 0.24. Experiment results show that a maximum secure key length obtained from our system, which ignores eavesdropping cases, is 125 with 20% decoy states and 82 with 50% decoy states for mean photon number of 0.794 for signal states and 1.588 for decoy states.