Relativistic quantum cryptography for open space without clock synchronization on the receiver and transmitter sides

The security of keys in quantum cryptography is based on fundamental quantum mechanical exclusions (the exclusion of cloning and copying of nonorthogonal quantum states. The physical type of a quantum object that carries information (photon, electron, atom, etc.) is insignificant; only its state vector is important. In relativistic quantum cryptography for open space, both the time of the information carrier (photon that propagates with the extremely allowable velocity in a vacuum) and its quantum state are of fundamental importance. Joint fundamental constraints that are dictated by both special relativity and quantum mechanics on the discrimination of nonorthogonal quantum states allow one to formulate fundamentally new key distribution protocols that are stable against any attacks on a key and guarantee the security of keys for a nonstrictly single-photon source and any losses in the communication channel. Although this protocol is a real-time protocol in the Minkowski space-time, where the attack to the communication channel is detected by the delay of eavesdropper measurement results, the protocol does not require clock synchronization on the transmitter and receiver sides.     

On the privacy-preserving cascade method for correcting errors in primary keys in quantum cryptography

A general method is proposed for privacy protection upon correction of errors in primary keys in quantum cryptography through an open communication channel. By the example of the cascade procedure for correcting errors, a method is described for removing information sent through an open communication channel when cleaning a key. The critical percentage is found for the quantum cryptography protocol BB84 to which the cascade error correction method with deletion guarantees the security of the final key. The method proposed for removing information sent through the open communication channel is quite general and can be used for many cleaning protocols for primary keys in quantum cryptography.     

On a solution to the problem of ensuring the security of quantum cryptography for an infinite communication channel

Quantum cryptography involves the fundamental question of the existence of secure protocols of quantum key distribution at any length of a communication channel (at any losses in it). A remarkable feature and novelty of the proposed protocol is that it ensures dual control; first, the intensity of a reference (intense) quantum state is controlled classically before the comparison (measurement) of coherent states from different time windows, and, second, the loss of coherence of a state is detected by interference measurements of an information quantum state and the reference quantum state tested against the conservation of the intensity. Thus, this is the only existing protocol stable to any losses in the communication channel. The length of the communication channel is limited only by dark noise in detectors.     

On protection against a bright-pulse attack in the two-pass quantum cryptography system

The security of keys in quantum cryptography systems, in contrast to mathematical cryptographic algorithms, is guaranteed by fundamental quantum-mechanical laws. However, the cryptographic resistance of such systems, which are distributed physical devices, fundamentally depends on the method of their implementation and particularly on the calibration and control of critical parameters. The most important parameter is the number of photons in quasi-single-photon information states in a communication channel. The sensitivity to a bright-pulse attack has been demonstrated in an explicit form for a number of systems. A method guaranteeing the resistance to such attacks has been proposed and implemented. Furthermore, the relation of physical observables used and obtained at the control of quantum states to the length of final secret keys has been obtained for the first time.     

Mesoscopic quantum cryptography

Since a strictly single-photon source is not yet available, in quantum cryptography systems, one uses, as information quantum states, coherent radiation of a laser with an average number of photons of μ ≈ 0.1–0.5 in a pulse, attenuated to the quasi-single-photon level. The linear independence of a set of coherent quasi-single-photon information states leads to the possibility of unambiguous measurements that, in the presence of losses in the line, restrict the transmission range of secret keys. Starting from a certain value of critical loss (the length of the line), the eavesdropper knows the entire key, does not make errors, and is not detected—the distribution of secret keys becomes impossible. This problem is solved by introducing an additional reference state with an average number of photons of μ_cl ≈ 10³–10⁶, depending on the length of the communication line. It is shown that the use of a reference state does not allow the eavesdropper to carry out measurements with conclusive outcome while remaining undetected. A reference state guarantees detecting an eavesdropper in a channel with high losses. In this case, information states may contain a mesoscopic average number of photons in the range of μ _q ≈ 0.5–10². The protocol proposed is easy to implement technically, admits flexible adjustment of parameters to the length of the communication line, and is simple and transparent for proving the secrecy of keys.     

Quantum cryptography with entangled photons

By realizing a quantum cryptography system based on polarization entangled photon pairs we establish highly secure keys, because a single photon source is approximated and the inherent randomness of quantum measurements is exploited. We implement a novel key distribution scheme using Wigner's inequality to test the security of the quantum channel, and, alternatively, realize a variant of the BB84 protocol. Our system has two completely independent users separated by 360 m, and generates raw keys at rates of 400-800 bits/s with bit error rates around 3%.     

Robustness of quantum cryptography: SARG04 key-distribution protocol

The SARG04 protocol is aimed at the improvement of the robustness of the main protocols in quantum cryptography (primarily, BB84 and B92) against the PNS attack in the case of the application of weak coherent pulses instead of the one-particle signals. An optimal attack of eavesdropper on the transmitted key is explicitly constructed for arbitrary angles between the basis states. A critical error up to which the key distribution is possible and the length of the final key are determined.     

On the quantum-mechanical bound on the loss of information through side channels in quantum cryptography

The security of cryptographic keys in quantum cryptography systems is guaranteed by fundamental quantum mechanical exclusion principles. A quantum channel through which quantum states are transferred is not controlled and an eavesdropper can perform any modifications with it. The security of quantum key distribution protocols has already been proved [M. Tomamichel et al., Nature Commun. 3, 634 (2011); S. N. Molotkov, J. Exp. Theor. Phys. 115, 969 (2012)], including the realistic case of a finite length of transmitted sequences. It is always assumed that the eavesdropper has neither direct nor indirect access to the transmitting and receiving equipment. The real situation is somewhat different. The preparation and detection of quantum states occur according to random sequences that are generated on the transmitter and receiver sides. Detecting electromagnetic radiation generated in these processes, the eavesdropper can obtain additional information on a key. The upper quantum-mechanical bound on the amount of information of the eavesdropper on the key that can be obtained through a side channel has been determined.     

Unconditional security of practical quantum key distribution

We present a complete protocol for BB84 quantum key distribution for a realistic setting (noise, loss, multi-photon signals of the source) that covers many of todays experimental implementations. The security of this protocol is shown against an eavesdropper having unrestricted power to manipulate the signals coherently on their path from sender to receiver. The protocol and the security proof take into account the effects concerning the finite size of the generated key. This paper is identical to the preprint arXiv:quant-ph/0107017, which was finalized in 2001. Therefore, some of the more recent developments, including the question of composability, are not addressed.     

What fundamentally new properties are introduced by special relativity to quantum cryptography in open space?

A fundamentally new relativistic quantum cryptography protocol has been proposed for key distribution through open space. The protocol guarantees the security of keys at any damping and for a nonstrictly single-photon source of quantum states.     

Quantum key distribution protocol using dense coding of three-qubit W state

The three-qubit W state, with an important feature that each pair of it’s qubits has the same and maximum amount of bipartite entanglement, can be reduced to an entangled 2-qubit system if one of its qubits is lost. Recently, Xue et al. proposed a three-party quantum secret sharing (QSS) protocol based on the three-qubit W state [Chinese Phys. 15, 7 (2006)]. Also, Joo et al. proposed a pair-wise quantum key distribution protocol among three users based on a special measurement on the three-qubit W state [eprint arXiv:quant-ph/0204003v2 (2002)]. This study aims to propose a novel quantum key distribution protocol (QKDP) for arbitrary two communications based on the dense coding and the special measurement of three-qubit W state with the X basis and the Z basis.     

Quantum key distribution with multi letter alphabets

We present a new protocol for continuous variable quantum key distribution (CV QKD). The novelty of the protocol is a multi letter alphabet represented by coherent states of light with a fixed amplitude and variable phase. Information is encoded in the phase of a coherent state which can be chosen from a regular discrete set consisting, however, of an arbitrary number of letters. We evaluate the security of the protocol against the beam splitting attack. As a result we show the proposed protocol has advantages over the standard two letter coherent state QKD protocol, especially in the case when losses in the communication channel are low.     

Relativistic quantum cryptography

A new protocol of quantum key distribution is proposed to transmit keys through free space. Along with quantum-mechanical restrictions on the discernibility of nonorthogonal quantum states, the protocol uses additional restrictions imposed by special relativity theory. Unlike all existing quantum key distribution protocols, this protocol ensures key secrecy for a not strictly one-photon source of quantum states and an arbitrary length of a quantum communication channel.     

量子BB84协议在联合旋转噪音信道上的安全性分析

多数在理想条件下设计的量子密码协议没有考虑实际通信中噪音的影响,可能造成机密信息不能被准确传输,或可能存在窃听隐藏在噪音中的风险,因此分析噪音条件下量子密码协议的安全性具有重要的意义.为了分析量子BB84协议在联合旋转噪音信道上的安全性,本文采用粒子偏转模型,对量子信道中的联合噪音进行建模,定量地区分量子信道中噪音和窃听干扰;并且采用冯·诺依曼熵理论建立窃听者能窃取的信息量与量子比特误码率、噪音水平三者之间的函数关系,定量地分析噪音条件下量子信道的安全性;最后根据联合噪音模型及窃听者能窃取的信息量与量子比特误码率、噪音水平三者之间的关系,定量地分析了量子BB84协议在联合噪音条件下的安全性并计算噪音临界点.通过分析可知,在已有噪音水平条件下,窃听者最多能够从通信双方窃取25%的密钥,但是Eve的窃听行为会被检测出来,这样Alice和Bob会放弃当前协商的密钥,重新进行密钥协商,直至确认没有Eve的窃听为止.这个结果说明量子BB84协议在联合旋转噪音信道下的通信是安全的.     

Nonclassical Attack on a Quantum Key Distribution System

The article is focused on research of an attack on the quantum key distribution system and proposes a countermeasure method. Particularly noteworthy is that this is not a classic attack on a quantum protocol. We describe an attack on the process of calibration. Results of the research show that quantum key distribution systems have vulnerabilities not only in the protocols, but also in other vital system components. The described type of attack does not affect the cryptographic strength of the received keys and does not point to the vulnerability of the quantum key distribution protocol. We also propose a method for autocompensating optical communication system development, which protects synchronization from unauthorized access. The proposed method is based on the use of sync pulses attenuated to a photon level in the process of detecting a time interval with a signal. The paper presents the results of experimental studies that show the discrepancies between the theoretical and real parameters of the system. The obtained data allow the length of the quantum channel to be calculated with high accuracy.     

On the resistance of relativistic quantum cryptography in open space at finite resources

The security of keys for the basic nonrelativistic BB84 protocol has been examined for more than 15 years. A simple proof of security for the case of a single-photon source of quantum states and finite sequences has been only recently obtained using entropy uncertainty relations. However, the existing sources of states are not strictly single-photon. Since sources are not single-photon and losses in a quantum channel??open space??are not a priori known and vary, nonrelativistic quantum cryptographic systems in open space cannot guarantee the unconditional security of keys. Recently proposed relativistic quantum cryptography removes fundamental constraints associated with non-single-photon sources and losses in open space. The resistance of a fundamentally new family of protocols for relativistic quantum key distribution through open space has been analyzed for the real situation with finite lengths of transmitted sequences of quantum states. This system is stable with real sources of non-single-photon states (weakened laser radiation) and arbitrary losses in open space.     

Distinguishability of quantum states and shannon complexity in quantum cryptography

The proof of the security of quantum key distribution is a rather complex problem. Security is defined in terms different from the requirements imposed on keys in classical cryptography. In quantum cryptography, the security of keys is expressed in terms of the closeness of the quantum state of an eavesdropper after key distribution to an ideal quantum state that is uncorrelated to the key of legitimate users. A metric of closeness between two quantum states is given by the trace metric. In classical cryptography, the security of keys is understood in terms of, say, the complexity of key search in the presence of side information. In quantum cryptography, side information for the eavesdropper is given by the whole volume of information on keys obtained from both quantum and classical channels. The fact that the mathematical apparatuses used in the proof of key security in classical and quantum cryptography are essentially different leads to misunderstanding and emotional discussions [1]. Therefore, one should be able to answer the question of how different cryptographic robustness criteria are related to each other. In the present study, it is shown that there is a direct relationship between the security criterion in quantum cryptography, which is based on the trace distance determining the distinguishability of quantum states, and the criterion in classical cryptography, which uses guesswork on the determination of a key in the presence of side information.     

量子密钥分发与量子安全直接通信

量子通信具有高安全性等优点,是当前的国际研究前沿,量子安全直接通信和量子密钥分发是两种重要的量子信息方式.量子密钥分发通过量子信道产生随机的密钥,而量子安全直接通信直接在量子信道中传输秘密信息.本文力图利用浅显易懂的语言介绍量子安全直接通信和量子密钥分发的基本原理;重点描述几个典型的量子安全直接通信方案,介绍目前的发展状态并展望未来.     

Multi-Bit Quantum Private Query

Most of the existing Quantum Private Queries (QPQ) protocols provide only single-bit queries service, thus have to be repeated several times when more bits are retrieved. Wei et al.'s scheme for block queries requires a high-dimension quantum key distribution system to sustain, which is still restricted in the laboratory. Here, based on Markus Jakobi et al.'s single-bit QPQ protocol, we propose a multi-bit quantum private query protocol, in which the user can get access to several bits within one single query. We also extend the proposed protocol to block queries, using a binary matrix to guard database security. Analysis in this paper shows that our protocol has better communication complexity, implementability and can achieve a considerable level of security.     

Multi-Bit Quantum Private Query

Most of the existing Quantum Private Queries(QPQ) protocols provide only single-bit queries service,thus have to be repeated several times when more bits are retrieved. Wei et al.'s scheme for block queries requires a high-dimension quantum key distribution system to sustain, which is still restricted in the laboratory. Here, based on Markus Jakobi et al.'s single-bit QPQ protocol, we propose a multi-bit quantum private query protocol, in which the user can get access to several bits within one single query. We also extend the proposed protocol to block queries, using a binary matrix to guard database security. Analysis in this paper shows that our protocol has better communication complexity, implementability and can achieve a considerable level of security.