Ideal quantum key distribution (QKD) protocols call for a source that emits single photon signals, but the sources used in typical practical realizations emit weak coherent states instead. A weak coherent state may contain more than one photon, which poses a potential security risk. QKD with weak coherent state signals has nevertheless been proven to be secure, but only under the assumption that the phase of each signal is random (and completely unknown to the adversary). Since this assumption need not be fully justified in practice, it is important to know whether phase randomization is really a requirement for security rather than a convenient technical assumption that makes the security proof easier. Here, we exhibit an explicit attack in which the eavesdropper exploits knowledge of the phase of the signals, and show that this attack allows the eavesdropper to learn every key bit in a parameter regime where a protocol using phase-randomized signals is provably secure. Thus we demonstrate that phase randomization really does enhance the security of QKD using weak coherent states. This result highlights the importance of a careful characterization of the source for proofs of the security of quantum key distribution.
We prove the unconditional security of coherent-state-based differential phase shift quantum key distribution protocol (DPSQKD) with block-wise phase randomization. Our proof is based on the conversion of DPSQKD to an equivalent entanglement-distillation protocol where the estimated phase error rate determines the amount of the privacy amplification. The generated final key has a contribution from events where the sender emits two or more photons, indicating the robustness of DPSQKD against photon-number-splitting attacks.
This paper proposes the first mediated semi-quantum key distribution in randomization-based environment with an untrusted third party(TP) who has the complete quantum capabilities to help two classical users to establish a secure key. The entanglement swapping between the collapsed qubits of Bell states and the Bell states is used to facilitate the design of the RSQKD protocol.
Phase randomization is an important assumption made in many security proofs of practical quantum key distribution (QKD) systems. Here, we present the first experimental demonstration of QKD with reliable active phase randomization. One key contribution is a polarization-insensitive phase modulator, which we added to a commercial phase-coding QKD system to randomize the global phase of each bit. We also proposed a simple but useful method to verify experimentally that the phase is indeed randomized. Our result shows very low QBER (<1%). We expect this active phase randomization process to be a …
Twin-field (TF) quantum key distribution (QKD) was conjectured to beat the private capacity of a point-to-point QKD link by using single-photon interference in a central measuring station. This remarkable conjecture has recently triggered an intense research activity to prove its security. Here, we introduce a TF-type QKD protocol which is conceptually simpler than the original proposal. It relies on local phase randomization, instead of global phase randomization, which significantly simplifies its security analysis and is arguably less demanding experimentally. We demonstrate that the secure…
Quantum key distribution(QKD) allows two remote parties to share information-theoretic secret keys. Many QKD protocols assume the phase of encoding state can be continuous randomized from 0 to 2 pi, which, however, may be questionable in experiment. This is particularly the case in the recently proposed twin-field(TF) QKD, which has received a lot of attention, since it can increase key rate significantly and even beat some theoretical rate-loss limits. As an intuitive solution, one may introduce discrete phase-randomization instead of continuous one. However, a security proof for a QKD protoc…
Twin-field (TF) quantum key distribution (QKD) can overcome fundamental secret-key-rate bounds on point-to-point QKD links, allowing us to reach longer distances than ever before. Since its introduction, several TF-QKD variants have been proposed, and some of them have already been implemented experimentally. Most of them assume that the users can emit weak coherent pulses with a continuous random phase. In practice, this assumption is often not satisfied, which could open up security loopholes in their implementations. To close this loophole, we propose and prove the security of a TF-QKD vari…
We improve the flexibility in designing access structures of quantum stabilizer-based secret sharing schemes for classical secrets, by introducing message randomization in their encoding procedures. We generalize the Gilbert-Varshamov bound for deterministic encoding to randomized encoding of classical secrets. We also provide an explicit example of a ramp secret sharing scheme with which multiple symbols in its classical secret are revealed to an intermediate set, and justify the necessity of incorporating strong security criterion of conventional secret sharing. Finally, we propose an explic…
Quantum key distribution (QKD) provides means for unconditional secure key transmission between two distant parties. However, in practical implementations, it suffers from quantum hacking due to device imperfections. Here we propose a hybrid measurement attack, with only linear optics, homodyne detection, and single photon detection, to the widely used vacuum+weak decoy state QKD system when the phase of source is partially randomized. Our analysis shows that, in some parameter regimes, the proposed attack would result in an entanglement breaking channel but still be able to trick the legitima…
In the classical setting, public-key encryption requires randomness in order to be secure against a forward search attack, whereby an adversary compares the encryption of a guess of the secret message with that of the actual secret message. We show that this is also true in the information-theoretic setting -- where the public keys are quantum systems -- by defining and giving an example of a forward search attack for any deterministic quantum-public-key bit-encryption scheme. However, unlike in the classical setting, we show that any such deterministic scheme can be used as a black box to bui…
Ping-Pong protocol is a type of quantum key distribution which makes use of two entangled photons in the EPR state. Its security is based on the randomization of the operations that Alice performs on the travel photon (qubit), and on the anti-correlation between the two photons in the EPR state. In this paper, we study the security of this protocol against some known quantum attacks, and present a scheme that may enhance its security to some degree.
Quantum key distribution (QKD) utilizes the laws of quantum mechanics to achieve information-theoretically secure key generation. This field is now approaching the stage of commercialization, but many practical QKD systems still suffer from security loopholes due to imperfect devices. In fact, practical attacks have successfully been demonstrated. Fortunately, most of them only exploit detection-side loopholes which are now closed by the recent idea of measurement-device-independent QKD. On the other hand, little attention is paid to the source which may still leave QKD systems insecure. In th…
We propose and experimentally demonstrate a scheme to render the detection apparatus of a Quantum Key Distribution system immune to the main classes of hacking attacks in which the eavesdropper explores the back-door opened by the single-photon detectors. The countermeasure is based on the creation of modes that are not deterministically accessible to the eavesdropper. We experimentally show that the use of beamsplitters and extra single-photon detectors at the receiver station passively creates randomized spatial modes that erase any knowledge the eavesdropper might have gained when using bri…
Coherent state photon sources are widely used in quantum information processing. In many applications, such as quantum key distribution (QKD), a coherent state is functioned as a mixture of Fock states by assuming its phase is continuously randomized. In practice, such a crucial assumption is often not satisfied and, therefore, the security of existing QKD experiments is not guaranteed. To bridge this gap, we provide a rigorous security proof of QKD with discrete-phase-randomized coherent state sources. Our results show that the performance of the discrete-phase randomization case is close to …
The potential weakness of the Y-00 direct encryption protocol when the encryption box ENC in Y-00 is not chosen properly is demonstrated in a fast correlation attack by S. Donnet et al in Phys. Lett. A 35, 6 (2006) 406-410. In this paper, we show how this weakness can be eliminated with a proper design of ENC. In particular, we present a Y-00 configuration that is more secure than AES under known-plaintext attack. It is also shown that under any ciphertext-only attack, full information-theoretic security on the Y-00 seed key is obtained for any ENC when proper deliberate signal randomization i…
Measurement-device-independent quantum key distribution removes all detector-side attacks in quantum cryptography, and in the meantime doubles the secure distance. The source side, however, is still vulnerable to various attacks. In particular, the continuous phase randomization assumption on the source side is normally not fulfilled in experimental implementation and may potentially open a loophole. In this work, we first show that indeed there are loopholes for imperfect phase randomization in measurement-device-independent quantum key distribution by providing a concrete attack. Then we pro…
Randomization of quantum states is the quantum analogue of the classical one-time pad. We present an improved, efficient construction of an approximately randomizing map that uses O(d/epsilon^2) Pauli operators to map any d-dimensional state to a state that is within trace distance epsilon of the completely mixed state. Our bound is a log d factor smaller than that of Hayden, Leung, Shor, and Winter (2004), and Ambainis and Smith (2004). Then, we show that a random sequence of essentially the same number of unitary operators, chosen from an appropriate set, with high probability form an approx…
Twin-field quantum key distribution (TF-QKD) protocol and its variants, e.g. phase-matching (PM) QKD and TF-QKD based on sending or not sending, are highly attractive since they are able to overcome the well-known rate-loss limit for QKD protocols without repeater: $R=O(η)$ with $η$ standing for the channel transmittance. However, all these protocols require active phase randomization and post-selection that play an essential role together in their security proof. Counterintuitively, we find that in TF-QKD, beating the rate-loss limit is still possible even if phase randomization and post-sele…
Among many quantum key distribution (QKD) protocols, the round-robin differential phase shift (RRDPS) protocol is unique in that it can upper-bound the amount of the information leakage without monitoring the signal disturbance. To expedite implementation of the protocol, however, the number of pulses forming a single block should be kept small, which significantly decreases the key rates in the original security proof. In the present paper, we refine the security proof of the RRDPS protocol in the finite-sized regime and achieve a tighter estimation for the information leakage without changin…
Quantum key distribution (QKD) allows two remote parties to share information-theoretically secure keys. In recent years, a revolutionary breakthrough called twin-field (TF) QKD has been developed to overcome the linear key-rate constraint and greatly increases the achievable distance. Phase-randomization and subsequent postselection play important roles in its security proof. Later, no-phase-postselection TF-QKD was proposed and became a popular variant, since the removal of phase postselection leads to a higher key rate. However, the achievable distance is decreased compared to the original …
Phase randomization is a very important assumption in the Bennett-Brassard 1984 quantum key distribution (QKD) system with a weak coherent source. Thus an active phase modulator is needed to randomize the phase of source. However, it is hard to check whether the phase of source is randomized totally or not in practical QKD systems. In this paper a partially random phase attack is proposed to exploit this imperfection. Our analysis shows that Eve can break the security of a two-way QKD system by using our attack, even if an active phase randomization is adopted by Alice. Furthermore, the numeri…
The security of source has become an increasingly important issue in quantum cryptography. Based on the framework of measurement-device-independent quantum-key-distribution (MDI-QKD), the source becomes the only region exploitable by a potential eavesdropper (Eve). Phase randomization is a cornerstone assumption in most discrete-variable (DV-) quantum communication protocols (e.g., QKD, quantum coin tossing, weak coherent state blind quantum computing, and so on), and the violation of such an assumption is thus fatal to the security of those protocols. In this paper, we show a simple quantum h…
It is repeatedly and persistently claimed in the literature that a specific trace criterion $d$ would guarantee universal composition security in quantum cryptography. Currently that is the sole basis of unconditional security claim in quantum key distribution. In this paper, it is shown that just security against known-plaintext attacks when the generated key is used in direct encryption is not provided by $d$. The problem is directly connected with several general problems in the existing unconditional security proofs in quantum key distribution. A number of issues will be clarified concerni…
Several fundamental issues in establishing security in continuous variable quantum key distribution are discussed, in particular on reverse reconciliation and security under heterodyne attack. It appears difficult to derive quantum advantage in a concrete realistic protocol due to source and loss uncertainties, apart from the problem of bounding Eve's information after reconciliation. The necessity of proving robust security for QKD protocols is indicated.
We propose various new techniques in quantum information theory, including a de Finetti style representation theorem for finite symmetric quantum states. As an application, we give a proof for the security of quantum key distribution which applies to arbitrary protocols.
This research note II introduces a way to understand a basic concept of the quantum enigma cipher. The conventional cipher is designed by a mathematical algorithm and its security is evaluated by the complexity of the algorithm in security analysis and ability of computers. This kind of cipher can be decrypted with probability one in principle by the Brute force attack in which an eavesdropper tries all the possible keys based on the correct ciphertext and some known plaintext. A cipher with quantum effects in physical layer may protect the system from the Brute force attack by means of the qu…
It is well known that Shor's quantum algorithm for integer factorization can break down the RSA public-key cryptosystem, which is widely used in many cryptographic applications. Thus, public-key cryptosystems in the quantum computational setting are longed for cryptology. In order to define the security notions of public-key cryptosystems, we have to model the power of the sender, receiver, adversary and channel. While we may consider a setting where quantum computers are available only to adversaries, we generally discuss what are the right security notions for (quantum) public-key cryptosyst…
Security of quantum key distribution against sophisticated attacks is among the most important issues in quantum information theory. In this work we prove security against a very important class of attacks called collective attacks (under a compatible noise model) which use quantum memories and gates, and which are directed against the final key. Although attacks stronger than the collective attacks can exist in principle, no explicit example was found and it is conjectured that security against collective attacks implies also security against any attack.
Long-distance quantum key distribution (QKD) has long time seriously relied on trusted relay or quantum repeater, which either has security threat or is far from practical implementation. Recently, a solution called twin-field (TF) QKD and its variants have been proposed to overcome this challenge. However, most security proofs are complicated, a majority of which could only ensure security against collective attacks. Until now, the full and simple security proof can only be provided with asymptotic resource assumption. Here, we provide a composable finite-key analysis for coherent-state-based…
We prove the security of a high-capacity quantum key distribution protocol over noisy channels. By using entanglement purification protocol, we construct a modified version of the protocol in which we separate it into two consecutive stages. We prove their securities respectively and hence the security of the whole protocol.
Modifications to a previous proof of the security of EPR-based quantum key distribution are proposed. This modified version applies to a protocol using three conjugate measurement bases rather than two. A higher tolerable error rate is obtained for the three-basis protocol.
We derive a proof of security for the Differential Phase Shift Quantum Key Distribution (DPSQKD) protocol under the assumption that Eve is restricted to individual attacks. The security proof is derived by bounding the average collision probability, which leads directly to a bound on Eve's mutual information on the final key. The security proof applies to realistic sources based on pulsed coherent light. We then compare individual attacks to sequential attacks and show that individual attacks are more powerful.
We propose a definition for the information theoretic security of a quantum public-key encryption scheme, and present bit-oriented and two-bit-oriented encryption schemes satisfying our security definition via the introduction of a new public-key algorithm structure. We extend the scheme to a multi-bitoriented one, and conjecture that it is also information theoretically secure, depending directly on the structure of our new algorithm.
This paper provides a security proof of the Bennett-Brassard (BB84) quantum key distribution protocol in practical implementation. To prove the security, it is not assumed that defects in the devices are absorbed into an adversary's attack. In fact, the only assumption in the proof is that the source is characterized. The proof is performed by lower-bounding adversary's Renyi entropy about the key before privacy amplification. The bound reveals the leading factors reducing the key generation rate.
Quantum Key Distribution (QKD) in principle offers unconditional security based on the laws of physics. Continuous variable (CV) quantum key distribution has the potential for high-key-rate and low-cost implementations using standard telecom components. Despite tremendous theoretical and experimental progress in continuous-variable quantum key distribution, the security has not been rigorously established for most current continuous-variable quantum key distribution systems that have imperfections. Among the imperfections, intensity fluctuation is a significant principal problem affecting secu…
We use the noisy entanglement-assisted classical capacity formula [arXiv:1609.08592] to create a coherent-attack security framework for Gaussian two-way quantum key distribution protocols in the asymptotic region.
We prove the security of quantum key distribution against the most general attacks which can be performed on the channel, by an eavesdropper who has unlimited computation abilities, and the full power allowed by the rules of classical and quantum physics. A key created that way can then be used to transmit secure messages in a way that their security is also unaffected in the future.
In this work we present a security analysis for quantum key distribution, establishing a rigorous tradeoff between various protocol and security parameters for a class of entanglement-based and prepare-and-measure protocols. The goal of this paper is twofold: 1) to review and clarify the state-of-the-art security analysis based on entropic uncertainty relations, and 2) to provide an accessible resource for researchers interested in a security analysis of quantum cryptographic protocols that takes into account finite resource effects. For this purpose we collect and clarify several arguments sp…
We consider the security of the Bennett-Brassard 1984 (BB84) protocol for Quantum Key Distribution (QKD), with arbitrary individual imperfections simultaneously in the source and detectors. We provide the secure key generation rate, and show that only two parameters must be bounded to ensure security; the basis dependence of the source and a detector blinding parameter. The system may otherwise be completely uncharacterized and contain large losses.
In this paper, we present an efficient implementation method of physical layer of Y-00 which can support a secure communication and a quantum key distribution (more generally key expansion) by IMDD(intensity modulation/direct detection) or FSK(frequency shift keying)optical fiber communication network. Although the general proof of the security is not yet given, a brief sketch of security analysis is shown, which involve an entanglement attack.
The security issues facing quantum key distribution (QKD) are explained, herein focusing on those issues that are cryptographic and information theoretic in nature and not those based on physics. The problem of security criteria is addressed. It is demonstrated that an attacker's success probabilities are the fundamental criteria of security that any theoretic security criterion must relate to in order to have operational significance. The errors committed in the prevalent interpretation of the trace distance criterion are analyzed. The security proofs of QKD protocols are discussed and assess…
We propose a proof of the security of EPR-based quantum key distribution against enemies with unlimited computational power. The proof holds for a protocol using interactive error-reconciliation scheme. We assume in this paper that the legitimate parties receive a given number of single photon signals and that their measurement devices are perfect.
Security proofs of quantum key distribution (QKD) typically assume that the devices of the legitimate users are perfectly shielded from the eavesdropper. This assumption is, however, very hard to meet in practice, and thus the security of current QKD implementations is not guaranteed. Here, we fill this gap by providing a finite-key security analysis for QKD which is valid against arbitrary information leakage from the state preparation process of the legitimate users. For this, we extend the techniques introduced in (New J. Phys. 18, 065008, (2016)) to the finite-key regime, and we evaluate t…
Two-way quantum key distribution protocols utilize bi-directional quantum communication to establish a shared secret key. Due to the increased attack surface, security analyses remain challenging. Here we investigate a high-dimensional variant of the Ping Pong protocol and perform an information theoretic security analysis in the finite-key setting. Our methods may be broadly applicable to other QKD protocols, especially those relying on two-way channels. Along the way, we show some fascinating benefits to high-dimensional quantum states applied to two-way quantum communication.
This paper provides a formula for the sacrifice bit-length for privacy amplification with the Bennett-Brassard 1984 protocol for finite key lengths when we employ the decoy method. Using the formula, we can guarantee the security parameter for realizable quantum key distribution system. The key generation rates with finite key lengths are numerically evaluated. The proposed method improves the existing key generation rate even in the asymptotic setting.
We analyse the finite-size security of the efficient Bennett-Brassard 1984 protocol implemented with decoy states and apply the results to a gigahertz-clocked quantum key distribution system. Despite the enhanced security level, the obtained secure key rates are the highest reported so far at all fibre distances.
We prove the security of the 1984 protocol of Bennett and Brassard (BB84) for quantum key distribution. We first give a key distribution protocol based on entanglement purification, which can be proven secure using methods from Lo and Chau's proof of security for a similar protocol. We then show that the security of this protocol implies the security of BB84. The entanglement-purification based protocol uses Calderbank-Shor-Steane (CSS) codes, and properties of these codes are used to remove the use of quantum computation from the Lo-Chau protocol.
Most security proofs of quantum key distribution (QKD) disregard the effect of information leakage from the users' devices, and, thus, do not protect against Trojan-horse attacks (THAs). In a THA, the eavesdropper injects strong light into the QKD apparatuses, and then analyzes the back-reflected light to learn information about their internal setting choices. Only a few recent works consider this security threat, but predict a rather poor performance of QKD unless the devices are strongly isolated from the channel. Here, we derive finite-key security bounds for decoy-state-based QKD schemes i…
We analyze the security against collective attacks for a homodyne-based continuous-variable quantum key distribution protocol using binary coherent states and postselection. We derive a lower bound of the secret key rate in an asymptotic scenario, and numerically optimize it for the case of a symmetric Gaussian channel.
In this paper we review a number of issues on the security of quantum key distribution (QKD) protocols that bear directly on the relevant physics or mathematical representation of the QKD cryptosystem. It is shown that the cryptosystem representation itself may miss out many possible attacks which are not accounted for in the security analysis and proofs. Hence the final security claims drawn from such analysis are not reliable, apart from foundational issues about the security criteria that are discussed elsewhere. The cases of continuous-variable QKD and multi-photon sources are elaborated u…
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.
Quantum key distribution protocols constitute an important part of quantum cryptography, where the security of sensitive information arises from the laws of physics. In this paper we introduce a new family of key distribution protocols and we compare its key with the well-known protocols such as BB84, PBC0 and generation rate to the well-known protocols such as BB84, PBC0 and R04. We also state the security analysis of these protocols based on the entanglement distillation and CSS codes techniques.
Rigorous mathematical proofs of the security of continuous-variable quantum key distribution (CV QKD) have been obtained recently. Unfortunately, these security proofs rely on assumptions that are hardly met in experimental practice. Here I investigate these issues in detail, and discuss experimentally-friendly workarounds to assess the security of CV QKD. The aim of this paper is to show that there are hidden and unsolved issues and to indicate possible partial solutions. To provide a complete and rigorous mathematical security proof is out of the scope of this contribution.
The existing unconditional security definitions of quantum key distribution (QKD) do not apply to joint attacks over QKD and the subsequent use of the resulting key. In this paper, we close this potential security gap by using a universal composability theorem for the quantum setting. We first derive a composable security definition for QKD. We then prove that the usual security definition of QKD still implies the composable security definition. Thus, a key produced in any QKD protocol that is unconditionally secure in the usual definition can indeed be safely used, a property of QKD that is h…
