Quantum key distribution (QKD) protocols are cryptographic techniques with security based only on the laws of quantum mechanics. Two prominent QKD schemes are the BB84 and B92 protocols that use four and two quantum states, respectively. In 2000, Phoenix et al. proposed a new family of three state protocols that offers advantages over the previous schemes. Until now, an error rate threshold for security of the symmetric trine spherical code QKD protocol has only been shown for the trivial intercept/resend eavesdropping strategy. In this paper, we prove the unconditional security of the trine spherical code QKD protocol, demonstrating its security up to a bit error rate of 9.81%. We also discuss on how this proof applies to a version of the trine spherical code QKD protocol where the error rate is evaluated from the number of inconclusive events.
By simulating four quantum key distribution (QKD) experiments and analyzing one decoy-state QKD experiment, we compare two data post-processing schemes based on security against individual attack by Lütkenhaus, and unconditional security analysis by Gottesman-Lo-Lütkenhaus-Preskill. Our results show that these two schemes yield close performances. Since the Holy Grail of QKD is its unconditional security, we conclude that one is better off considering unconditional security, rather than restricting to individual attacks.
This article describes a quantum bit commitment protocol, QBC1, based on entanglement destruction via forced measurements and proves its unconditional security.
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…
The commitment of bits between two mutually distrustful parties is a powerful cryptographic primitive with which many cryptographic objectives can be achieved. It is widely believed that unconditionally secure quantum bit commitment is impossible due to quantum entanglement cheating, which is codified in a general impossibility theorem. Gaps in the proof of this impossibility theorem are found. An unconditionally secure bit commitment protocol utilizing anonymous quantum states and the no-clone theorem is presented below with a full security proof.
We present an extension of the first proof for the unconditional security of the BB84 quantum key distribution protocol which was given by Mayers. We remove the constraint that a perfect BB84 quantum source is required and the proof given here covers a range of practical quantum sources. Nothing is assumed about the detector except that the efficiency with which signals are detected is basis independent.
In this Letter, we prove the unconditional security of single-photon differential phase shift quantum key distribution (DPS-QKD) protocol, based on the conversion to an equivalent entanglement-based protocol. We estimate the upper bound of the phase error rate from the bit error rate, and show that DPS-QKD can generate unconditionally secure key when the bit error rate is not greater than 4.12%. This proof is the first step to the unconditional security proof of coherent state DPS-QKD.
We derive a bound for the security of QKD with finite resources under one-way post-processing, based on a definition of security that is composable and has an operational meaning. While our proof relies on the assumption of collective attacks, unconditional security follows immediately for standard protocols like Bennett-Brassard 1984 and six-states. For single-qubit implementations of such protocols, we find that the secret key rate becomes positive when at least N\sim 10^5 signals are exchanged and processed. For any other discrete-variable protocol, unconditional security can be obtained us…
We prove the unconditional security of a quantum key distribution protocol in which bit values are encoded in the phase of a weak coherent-state pulse relative to a strong reference pulse. In contrast to implementations in which a weak pulse is used as a substitute for a single-photon source, the achievable key rate is found to decrease only linearly with the transmission of the channel.
We present a continuous-variable quantum key distribution protocol combining a discrete modulation and reverse reconciliation. This protocol is proven unconditionally secure and allows the distribution of secret keys over long distances, thanks to a reverse reconciliation scheme efficient at very low signal-to-noise ratio.
This article describes a quantum bit commitment protocol, QBC3, based on entanglement destruction via forced measurements and proves its unconditional security. Some comments on the current status of the field are also made.
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.
The problem of unconditional security of quantum cryptography (i.e. the security which is guaranteed by the fundamental laws of nature rather than by technical limitations) is one of the central points in quantum information theory. We propose a relativistic quantum cryptosystem and prove its unconditional security against any eavesdropping attempts. Relativistic causality arguments allow to demonstrate the security of the system in a simple way. Since the proposed protocol does not employ collective measurements and quantum codes, the cryptosystem can be experimentally realized with the prese…
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.
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.
It is generally believed that unconditionally secure quantum bit commitment is impossible, due to widespread acceptance of an impossibility proof that utilizes quantum entaglement cheating. In this paper, we delineate how the impossibiliy proof formulation misses various types of quantum bit commitment protocols based on two-way quantum communications. We point out some of the gaps in the impossibility proof reasoning, and present corresponding counterexamples. Four different types of bit commitment protocols are constructed with several new protocol techniques. A specific Type 4 protocol is d…
It has been widely claimed and believed that many protocols in quantum key distribution, especially the single-photon BB84 protocol, have been proved unconditionally secure at least in principle, for both asymptotic and finite protocols with realistic bit lengths. In this paper it is pointed out that the only known quantitative justification for such claims is based on incorrect assertions. The precise security requirements are described in terms of the attacker's sequence and bit error probabilities in estimating the key. The extent to which such requirements can be met from a proper trace di…
The ``impossibility proof'' on unconditionally secure quantum bit commitment is critically analyzed. Many possibilities for obtaining a secure bit commitment protocol are indicated, purely on the basis of two-way quantum communications, which are not covered by the impossibility proof formulation. They are classified under six new types of protocols, with security proofs for specific examples on four types. Reasons for some previously failed attempts at obtaining secure protocols are also indicated.
We present here an information theoretic study of Gaussian collective attacks on the continuous variable key distribution protocols based on Gaussian modulation of coherent states. These attacks, overlooked in previous security studies, give a finite advantage to the eavesdropper in the experimentally relevant lossy channel, but are not powerful enough to reduce the range of the reverse reconciliation protocols. Secret key rates are given for the ideal case where Bob performs optimal collective measurements, as well as for the realistic cases where he performs homodyne or heterodyne measuremen…
In a deterministic quantum key distribution (DQKD) protocol with a two-way quantum channel, Bob sends a qubit to Alice who then encodes a key bit onto the qubit and sends it back to Bob. After measuring the returned qubit, Bob can obtain Alice's key bit immediately, without basis reconciliation. Since an eavesdropper may attack the qubits traveling on either the Bob-Alice channel or the Alice-Bob channel, the security analysis of DQKD with a two-way quantum channel is complicated and its unconditional security has been controversial. This paper presents a security proof of a single-photon four…
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.
We prove unconditional security for a quantum key distribution (QKD) protocol based on distilling pbits (twisted ebits) [quant-ph/0309110] from an arbitrary untrusted state that is claimed to contain distillable key. Our main result is that we can verify security using only public communication -- via parameter estimation of the given untrusted state. The technique applies even to bound entangled states, thus extending QKD to the regime where the available quantum channel has zero quantum capacity. We also show how to convert our purification-based QKD schemes to prepare-measure schemes.
In this report, we simulate practical feature of Yuen-Kim protocol for quantum key distribution with unconditional secure. In order to demonstrate them experimentally by intensity modulation/direct detection(IMDD) optical fiber communication system, we use simplified encoding scheme to guarantee security for key information(1 or 0). That is, pairwise M-ary intensity modulation scheme is employed. Furthermore, we give an experimental implementation of YK protocol based on IMDD.
We prove the unconditional security of the original Bennett 1992 protocol with strong reference pulse. We show that we may place a projection onto suitably defined qubit spaces before the receiver, which makes the analysis as simple as qubit-based protocols. Unlike the single-photon-based qubits, the qubits identified in this scheme are almost surely detected by the receiver even after a lossy channel. This leads to the key generation rate that is proportional to the channel transmission rate for proper choices of experimental parameters.
We show that the security proof of the Bennett 1992 protocol over loss-free channel in (K. Tamaki, M. Koashi, and N. Imoto, Phys. Rev. Lett. 90, 167904 (2003)) can be adapted to accommodate loss. We assumed that Bob's detectors discriminate between single photon states on one hand and vacuum state or multi-photon states on the other hand.
Quantum key distribution is widely thought to offer unconditional security in communication between two users. Unfortunately, a widely accepted proof of its security in the presence of source, device and channel noises has been missing. This long-standing problem is solved here by showing that, given fault-tolerant quantum computers, quantum key distribution over an arbitrarily long distance of a realistic noisy channel can be made unconditionally secure. The proof is reduced from a noisy quantum scheme to a noiseless quantum scheme and then from a noiseless quantum scheme to a noiseless class…
A simple proof of the unconditional security of a relativistic quantum cryptosystem based on orthogonal states is proposed. Restrictions imposed by special relativity allow to substantially simplify the proof compared with the non-relativistic cryptosystems involving non-orthogonal states. Important for the proposed protocol is the spatio-temporal structure of the quantum states which is actually ignored in the non-relativistic protocols employing only the structure of the state space of the information carriers. As a consequence, the simplification arises because of the inefficiency of collec…
By using local quantum teleportation of a fixed state to one qubit of an entangled pair sent from the other party, it is shown how one party can commit a bit with only classical information as evidence that results in an unconditionally secure protocol. The well-known ``impossibility proof'' does not cover such protocols due to its different commitment and opening prescriptions, which necessitate actual quantum measurements among different possible systems that cannot be entangled as a consequence.
We propose the improved decoy state quantum key distribution incorporating finite statistics due to the finite code length and report on its demonstration. In our experiment, four different intensities including the vacuum state for optimal pulses are used and the key generation rate of 200 bps is achieved in the 20 km telecom optical fiber transmission keeping the eavesdropper's mutual information with the final key less than 2^{-9}.
The Sending-or-Not-Sending protocol of the twin-field quantum key distribution (TF-QKD) has its advantage of unconditional security proof under any coherent attack and fault tolerance to large misalignment error. So far this is the only coherent-state based TF-QKD protocol that has considered finite-key effect, the statistical fluctuations. Here we consider the complete finite-key effects for the protocol and we show by numerical simulation that the protocol with typical finite number of pulses in practice can produce unconditional secure final key under general attack, including all coherent …
We show how to use decoherence-free subspaces over collective-noise quantum channels to convey classical information in perfect secrecy. We argue that codes defined over decoherence-free subspaces are codes for quantum wiretap channels in which the gain of information by a non-authorized receiver is zero. We also show that if some symmetry conditions are guaranteed, the maximum rate on which these secret communications take place is equal to the Holevo-Schumacher-Westmoreland capacity of the quantum channel.
We propose an unconditionally secure quantum key distribution (QKD) protocol, which uses a relatively strong signal pulse. While our protocol shares similar security bases as the Bennett 1992 protocol with a strong reference pulse (B92), our scheme uses a smaller number of detectors and it is robust against Rayleigh scattering in an optical fibre. We derive a lower bound of secret key generation rate of our protocol and show that our protocol can cover relatively long distances, assuming precise phase modulations and stable interferometers.
A class of quantum protocols of bit commitment is constructed based on the nonorthogonal states coding and the correlation immunity of some Boolean functions. The binding condition of these protocols is guaranteed mainly by the law of causality and the concealing condition is guaranteed by the indistinguishability between nonorthogonal quantum states and the correlation immunity of Boolean functions. We also give out an oblivious transfer protocol based on two-nonorthogonal states coding and build a bit commitment protocol on top of it. The relationship between these protocols and the well kno…
So far, unconditional security in key distribution processes has been confined to quantum key distribution (QKD) protocols based on the no-cloning theorem of nonorthogonal bases. Recently, a completely different approach, the unconditionally secured classical key distribution (USCKD), has been proposed for unconditional security in the purely classical regime. Unlike QKD, both classical channels and orthogonal bases are key ingredients in USCKD, where unconditional security is provided by deterministic randomness via path superposition-based reversible unitary transformations in a coupled Mach…
We prove the unconditional security of a quantum key distribution (QKD) protocol on a noisy channel against the most general attack allowed by quantum physics. We use the fact that in a previous paper we have reduced the proof of the unconditionally security of this QKD protocol to a proof that a corresponding Quantum String Oblivious Transfer (String-QOT) protocol would be unconditionally secure against Bob if implemented on top of an unconditionally secure bit commitment scheme. We prove a lemma that extends a security proof given by Yao for a (one bit) QOT protocol to this String-QOT protoc…
The need for secrecy and security is essential in communication. Secret sharing is a conventional protocol to distribute a secret message to a group of parties, who cannot access it individually but need to cooperate in order to decode it. While several variants of this protocol have been investigated, including realizations using quantum systems, the security of quantum secret sharing schemes still remains unproven almost two decades after their original conception. Here we establish an unconditional security proof for continuous variable entanglement-based quantum secret sharing schemes, in …
An unconditionally secure quantum cion tossing protocol for two remote participants via entangled swapping is presented. The security of this protocol is guaranteed by the nonlocal property of quantum entanglement and the classical complexity.
Spacetime-constrained oblivious transfer (SCOT) extends the fundamental primitive of oblivious transfer to Minkowski space. SCOT and location oblivious data transfer (LODT) are the only known cryptographic tasks with classical inputs and outputs for which unconditional security needs both quantum theory and relativity. We give an unconditionally secure SCOT protocol that, contrasting previous SCOT and LODT protocols, is practical to implement with current technology, where distant agents need only communicate classical information, while quantum communication occurs at a single location. We al…
It is shown how the evidence state space in quantum bit commitment may be made to depend on the bit value 0 or 1 with split entangled pairs. As a consequence, one can obtain a protocol that is perfectly concealing, but is also $ε$-binding because the bit-value dependent evidence space prevents the committing party from cheating by means of a local transformation that is independent of the part of evidence state space that has never been in his possession.
Quantum cryptography is a major ingredient of the future quantum internet that promises various secure communication tasks. Quantum conference key agreement (CKA) is an important cryptographic primitive of quantum cryptography, which provides the conference key among multiple users simultaneously. However, quantum CKA is currently far from practical application due to the low conference key rate. Here, we propose a quantum CKA protocol of three users with information-theoretic security. Our protocol only requires phase-randomized weak coherent sources and threshold single-photon detectors, and…
Basic techniques to prove the unconditional security of quantum cryptography are described. They are applied to a quantum key distribution protocol proposed by Bennett and Brassard in 1984. The proof considers a practical variation on the protocol in which the channel is noisy and photons may be lost during the transmission. The initial coding into the channel must be perfect (i.e., exactly as described in the protocol). No restriction is imposed on the detector used at the receiving side of the channel, except that whether or not the received system is detected must be independent of the basi…
We prove the unconditional security of the standard six-state scheme for quantum key distribution (QKD). We demonstrate its unconditional security up to a bit error rate of 12.7 percents, by allowing only one-way classical communications in the error correction/privacy amplification procedure between Alice and Bob. This shows a clear advantage of the six-state scheme over another standard scheme---BB84, which has been proven to be secure up to only about 11 percents, if only one-way classical communications are allowed. Our proof technique is a generalization of that of Shor-Preskill's proof o…
The unconditional security of continuous-variable quantum key distribution is established for all schemes based on the estimation of the channel loss and excess noise. It is proved that, in the limit of large keys, Gaussian attacks are asymptotically optimal among the most general (coherent) attacks, where the transmission is tapped using arbitrary ancillas and stored in a quantum memory as a whole. Then, it is shown that the previously derived bounds on the achievable secret key rates against collective attacks remain asymptotically valid for arbitrary coherent attacks.
In this paper, we prove that the unconditionally secure key can be surprisingly extracted from {\it multi}-photon emission part in the photon polarization-based QKD. One example is shown by explicitly proving that one can indeed generate an unconditionally secure key from Alice's two-photon emission part in ``Quantum cryptography protocols robust against photon number splitting attacks for weak laser pulses implementations'' proposed by V. Scarani {\it et al.,} in Phys. Rev. Lett. {\bf 92}, 057901 (2004), which is called SARG04. This protocol uses the same four states as in BB84 and differs on…
A new cryptographic tool, anonymous quantum key technique, is introduced that leads to unconditionally secure key distribution and encryption schemes that can be readily implemented experimentally in a realistic environment. If quantum memory is available, the technique would have many features of public-key cryptography; an identification protocol that does not require a shared secret key is provided as an illustration. The possibility is also indicated for obtaining unconditionally secure quantum bit commitment protocols with this technique.
We devise a simple modification that essentially doubles the efficiency of the BB84 quantum key distribution scheme proposed by Bennett and Brassard. We also prove the security of our modified scheme against the most general eavesdropping attack that is allowed by the laws of physics. The first major ingredient of our scheme is the assignment of significantly different probabilities to the different polarization bases during both transmission and reception, thus reducing the fraction of discarded data. A second major ingredient of our scheme is a refined analysis of accepted data: We divide th…
Recently, new physics for unconditional security in a classical key distribution (USCKD) in a frame of a double Mach-Zehnder interferometer has been proposed and demonstrated as a proof of principle, where the unconditional security is unaffected by the no-cloning theorem of quantum key distribution protocols. Due to environmental phase fluctuations caused by temperature variations, atmospheric turbulences, or mechanical vibrations, active phase locking seems to be necessary for the two-channel transmission layout of USCKD. Here, the two-channel layout of USCKD is demonstrated to be an environ…
High-dimensional quantum key distribution (HDQKD) offers the possibility of high secure-key rate with high photon-information efficiency. We consider HDQKD based on the time-energy entanglement produced by spontaneous parametric downconversion, and show that it is secure against collective attacks. Its security rests upon visibility data -- obtained from Franson and conjugate-Franson interferometers -- that probe photon-pair frequency correlations and arrival-time correlations. From these measurements an upper bound can be established on the eavesdropper's Holevo information by translating the…
The claim of quantum cryptography has always been that it can provide protocols that are unconditionally secure, that is, for which the security does not depend on any restriction on the time, space or technology available to the cheaters. We show that this claim does not hold for any quantum bit commitment protocol. Since many cryptographic tasks use bit commitment as a basic primitive, this result implies a severe setback for quantum cryptography. The model used encompasses all reasonable implementations of quantum bit commitment protocols in which the participants have not met before, inclu…
We prove the unconditional security of the Bennett 1992 protocol, by using a reduction to an entanglement distillation protocol initiated by a local filtering process. The bit errors and the phase errors are correlated after the filtering, and we can bound the amount of phase errors from the observed bit errors by an estimation method involving nonorthogonal measurements. The angle between the two states shows a trade-off between accuracy of the estimation and robustness to noises.
A new relativistic quantum protocol is proposed allowing to implement the bit commitment scheme. The protocol is based on the idea that in the relativistic case the field propagation to the region of space accessible to measurement requires, contrary to the non-relativistic case, a finite non-zero time which depends on the structure of the particular state of the field. In principle, the secret bit can be stored for arbitrarily long time with the probability arbitrarily close to unit.
Storing data on an external server with information-theoretic security, while using a key shorter than the data itself, is impossible. As an alternative, we propose a scheme that achieves information-theoretically secure tamper evidence: The server is able to obtain information about the stored data, but not while staying undetected. Moreover, the client only needs to remember a key whose length is much shorter than the data. We provide a security proof for our scheme, based on an entropic uncertainty relation, similar to QKD proofs. Our scheme works if Alice is able to (reversibly) randomise …
Quantum key distribution is the most well-known application of quantum cryptography. Previous proposed proofs of security of quantum key distribution contain various technical subtleties. Here, a conceptually simpler proof of security of quantum key distribution is presented. The new insight is the invariance of the error rate of a teleportation channel: We show that the error rate of a teleportation channel is independent of the signals being transmitted. This is because the non-trivial error patterns are permuted under teleportation. This new insight is combined with the recently proposed qu…
Since unconditionally secure quantum two-party computations are known to be impossible, most existing quantum private comparison (QPC) protocols adopted a third party. Recently, we proposed a QPC protocol which involves two parties only, and showed that although it is not unconditionally secure, it only leaks an extremely small amount of information to the other party. Here we further propose the device-independent version of the protocol, so that it can be more convenient and dependable in practical applications.
This paper has been withdrawn by the authors,because the proposed protocol is still coverd by the no-go theorem of Mayers, Lo and Chau. We thank H-K. Lo and HF Chau for helpful correspondences.
Unconditional Security of Discrete-Modulated CV-QKD from Infinite-Dimensional MEAT
University of Waterloo（滑铁卢大学）；National University of Singapore（新加坡国立大学）；Technische Universität Wien（维也纳工业大学）；AIT Austrian Institute of Technology（奥地利技术研究院）
We present a quantum-public-key identification protocol and show that it is secure against a computationally-unbounded adversary. This demonstrates for the first time that unconditionally-secure and reusable public-key authentication is possible in principle with (pure-state) public keys.
Bit commitment is a fundamental cryptographic task that guarantees a secure commitment between two mutually mistrustful parties and is a building block for many cryptographic primitives, including coin tossing, zero-knowledge proofs, oblivious transfer and secure two-party computation. Unconditionally secure bit commitment was thought to be impossible until recent theoretical protocols that combine quantum mechanics and relativity were shown to elude previous impossibility proofs. Here we implement such a bit commitment protocol. In the experiment, the committer performs quantum measurements u…
Squeezed states of harmonic oscillators are a central resource for continuous-variable quantum sensing, computation and communication. Here we propose a method for the generation of very good approximations to highly squeezed vacuum states with low excess anti-squeezing using only a few oscillator-qubit coupling gates through a Rabi-type interaction Hamiltonian. This interaction can be implemented with several different methods, which has previously been demonstrated in superconducting circuit and trapped-ion platforms. The protocol is compatible with other protocols manipulating quantum harmo…
We consider the implementation of two-party cryptographic primitives based on the sole assumption that no large-scale reliable quantum storage is available to the cheating party. We construct novel protocols for oblivious transfer and bit commitment, and prove that realistic noise levels provide security even against the most general attack. Such unconditional results were previously only known in the so-called bounded-storage model which is a special case of our setting. Our protocols can be implemented with present-day hardware used for quantum key distribution. In particular, no quantum sto…
