The existance of unconditionally secure quantum bit commitment

Anonymous-key quantum cryptography and unconditionally secure quantum bit commitment

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.

使用修改的双缝和不稳定粒子的无条件安全量子比特承诺

Unconditionally secure quantum bit commitment using modified double-slit and unstable particles

指出无条件安全量子比特承诺不可行定理的模型非通用，利用不稳定粒子和修改的双缝装置构造了无需传输量子态的无条件安全协议。

Quantum Bit Commitment can be Unconditionally Secure

It is generally believed that unconditionally secure quantum bit commitment (QBC) is proven impossible by a "no-go theorem". We point out that the theorem only establishes the existence of a cheating unitary transformation in any QBC scheme secure against the receiver, but this fact alone is not sufficient to rule out unconditionally secure QBC as a matter of principle, because there exists no proof that the cheating unitary transformation must be known to the cheater in all possible cases. In this work, we show how to circumvent the "no-go theorem" and prove that unconditionally secure QBC is…

A simple unconditionally secure quantum bit commitment protocol via quantum teleportation

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.

Unconditionally Secure Quantum Bit Commitment

This paper has been withdrawn: it does not evade the no-go results of Mayers, Lo and Chau, to whom I am most grateful for helpful correspondences.

Unconditionally Secure Quantum Bit Commitment Using Neutron Double-Slit Interference

Using a neutron double-slit setup, we construct a quantum bit commitment scheme in which time development of quantum states plays an essential role. Our scheme evades the widely accepted no-go theorem by the fact that it is neither possible to stop the time evolution of spreading wave packets, nor is it possible to evolve them backward in time. Moreover, for unstable particles such as neutrons, one cannot delay detecting their positions indefinitely, or they would disintegrate spontaneously and escape detection. We find that using non-stationary states instead of stationary ones, unconditional…

Unconditionally secure quantum bit commitment is impossible

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…

Unconditionally Secure Quantum Bit Commitment Is Possible

Bit commitment involves the submission of evidence from one party to another so that the evidence can be used to confirm a later revealed bit value by the first party, while the second party cannot determine the bit value from the evidence alone. It is widely believed that secure quantum bit commitment is impossible due to quantum entanglement cheating, which is codified in a general impossibility theorem. In this paper, the scope of this general impossibility proof is extended and analyzed, and gaps are found. Three specific protocols are described for which the entanglement cheating as given…

Unconditionally secure commitment in position-based quantum cryptography

A new commitment scheme based on position-verification and non-local quantum correlations is presented here for the first time in literature. The only credential for unconditional security is the position of committer and non-local correlations generated; neither receiver has any pre-shared data with the committer nor does receiver require trusted and authenticated quantum/classical channels between him and the committer. In the proposed scheme, receiver trusts the commitment only if the scheme itself verifies position of the committer and validates her commitment through non-local quantum cor…

Unconditionally Secure Relativistic Quantum Bit Commitment

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.

Unconditionally secure bit commitment by causally independent encryptions

We propose a new classical bit commitment protocol using the relativistic constraint that signals cannot travel faster than the speed of light $c$. This protocol is unconditionally secure against both classical or quantum attacks. The sender (Alice) and the receiver (Bob) each controls two secure stations separated by a large distance $d$, and they communicate by exchanging classical information only. Alice commits by sending from her stations two causally independent encrypted messages to the neighboring Bob's stations, after that the protocol is out of her control and she plays no role in th…

Unconditionally Secure Quantum Bit Commitment Protocols Based on Correlation Immune Boolean Function

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…

Experimental unconditionally secure bit commitment

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…

Another simple unconditionally secure quantum bit commitment protocol -- beating entanglement with entanglement

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.

Unconditionally secure quantum bit commitment based on the uncertainty principle

Unconditionally secure quantum bit commitment (QBC) was considered impossible. But the no-go proofs are based on the Hughston-Jozsa-Wootters (HJW) theorem (a.k.a. the Uhlmann theorem). Recently it was found that in high-dimensional systems, there exist some states which can display a chaos effect in quantum steering, so that the attack strategy based on the HJW theorem has to require the capability of discriminating quantum states with very subtle difference, to the extent that is not allowed by the uncertainty principle. With the help of this finding, here we propose a simple QBC protocol whi…

Quantum one-time tables for unconditionally secure qubit-commitment

The commodity-based cryptography is an alternative approach to realize conventionally impossible cryptographic primitives such as unconditionally secure bit-commitment by consuming pre-established correlation between distrustful participants. A unit of such classical correlation is known as the one-time table (OTT). In this paper, we introduce a new example besides quantum key distribution in which quantum correlation is useful for cryptography. We propose a scheme for unconditionally secure qubit-commitment, a quantum cryptographic primitive forbidden by the recently proven no-masking theorem…

How unconditionally secure quantum bit commitment is possible

Bit commitment involves the submission of evidence from one party to another so that the evidence can be used to confirm a later revealed bit value by the first party, while the second party cannot determine the bit value from the evidence alone. 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. In this paper, the scope of this general impossibility proof is analyzed, and gaps are found. Two variants of a bit commitment scheme utilizing anonymous quantum states and d…

Unconditional security in quantum bit commitment

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.

Unconditionally Secure Bit Commitment

We describe a new classical bit commitment protocol based on cryptographic constraints imposed by special relativity. The protocol is unconditionally secure against classical or quantum attacks. It evades the no-go results of Mayers, Lo and Chau by requiring from Alice a sequence of communications, including a post-revelation verification, each of which is guaranteed to be independent of its predecessor.

A brief review on the impossibility of quantum bit commitment

The desire to obtain an unconditionally secure bit commitment protocol in quantum cryptography was expressed for the first time thirteen years ago. Bit commitment is sufficient in quantum cryptography to realize a variety of applications with unconditional security. In 1993, a quantum bit commitment protocol was proposed together with a security proof. However, a basic flaw in the protocol was discovered by Mayers in 1995 and subsequently by Lo and Chau. Later the result was generalized by Mayers who showed that unconditionally secure bit commitment is impossible. A brief review on quantum bit…

带预处理的无条件安全量子承诺

Unconditionally secure quantum commitments with preprocessing

本研究提出借助量子辅助输入构建无需未证明复杂度假设的计算安全承诺方案，量子辅助输入可通过两种时间复杂度方式制备且无需可信第三方，突破了经典情形下需先证明$\textsf{P} \neq \textsf{NP}$的限制。

Unconditionally Secure Commitment of a Certified Classical Bit is Impossible

In a secure bit commitment protocol involving only classical physics, A commits either a 0 or a 1 to B. If quantum information is used in the protocol, A may be able to commit a state of the form $α\ket{0} + β\ket{1}$. If so, she can also commit mixed states in which the committed bit is entangled with other quantum states under her control. We introduce here a quantum cryptographic primitive, {\it bit commitment with a certificate of classicality} (BCCC), which differs from standard bit commitment in that it guarantees that the committed state has a fixed classical value. We show that no unco…

Unconditionally Secure Bit Commitment by Transmitting Measurement Outcomes

We propose a new unconditionally secure bit commitment scheme based on Minkowski causality and the properties of quantum information. The receiving party sends a number of randomly chosen BB84 qubits to the committer at a given point in space-time. The committer carries out measurements in one of the two BB84 bases, depending on the committed bit value, and transmits the outcomes securely at light speed in opposite directions to remote agents. These agents unveil the bit by returning the outcomes to adjacent agents of the receiver. The security proofs rely only on simple properties of quantum …

Quantum nonlocality as the route for ever-lasting unconditionally secure bit commitment

We present a bit commitment protocol based on quantum nonlocality that seems to bring ever-lasting unconditional security. Although security is not rigorously proved, physical arguments and numerical simulations support this conclusion. The key point is that the proof of the commitment is forced to become classical data uncorrelated with anything else. This allows us to circumvent previous impossibility proofs in which it is assumed that classical data can be replaced by quantum data that may be entangled with the committer. The proposed protocol also recovers two features missing in recent "r…

Why there is no impossibility theorem on Secure Quantum Bit Commitment

The impossibility proof on unconditionally secure quantum bit commitment is critically reviewed. Different ways of obtaining secure protocols are indicated.

Quantum bit commitment and unconditional security

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…

一种简单实用的量子比特承诺协议

A simple practical quantum bit commitment protocol

该研究提出一种实现难度与现有实用方案相当、但安全性更强的简单量子比特承诺协议，可在非完美绑定与隐藏条件下无限接近无条件完全安全。

No Superluminal Signaling Implies Unconditionally Secure Bit Commitment

Bit commitment (BC) is an important cryptographic primitive for an agent to convince a mutually mistrustful party that she has already made a binding choice of 0 or 1 but only to reveal her choice at a later time. Ideally, a BC protocol should be simple, reliable, easy to implement using existing technologies, and most importantly unconditionally secure in the sense that its security is based on an information-theoretic proof rather than computational complexity assumption or the existence of a trustworthy arbitrator. Here we report such a provably secure scheme involving only one-way classica…

具有量子辅助输入的无条件安全承诺

Unconditionally Secure Commitments with Quantum Auxiliary Inputs

本文在量子辅助输入模型和公共参考量子态模型中无条件构造了具有计算或统计安全性的量子承诺，绕过了统计安全不可能性，并给出相关密码学应用。

Quantum bit commitment protocol without quantum memory

Quantum protocols for bit commitment have been proposed and it is largely accepted that unconditionally secure quantum bit commitment is not possible; however, it can be more secure than classical bit commitment. In despite of its usefulness, quantum bit commitment protocols have not been experimentally implemented. The main reason is the fact that all proposed quantum bit commitment protocols require quantum memory. In this work, we show a quantum bit commitment protocol that does not require quantum memory and can be implemented with present technology.

Quantum Key Distribution and String Oblivious Transfer in Noisy Channels

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…

Defeating classical bit commitments with a quantum computer

It has been recently shown by Mayers that no bit commitment scheme is secure if the participants have unlimited computational power and technology. However it was noticed that a secure protocol could be obtained by forcing the cheater to perform a measurement. Similar situations had been encountered previously in the design of Quantum Oblivious Transfer. The question is whether a classical bit commitment could be used for this specific purpose. We demonstrate that, surprisingly, classical unconditionally concealing bit commitments do not help.

一种相对论量子承诺方案的不安全性

Insecurity of a relativistic quantum commitment scheme

本研究针对一种被声称无条件安全的相对论量子承诺方案，提出作弊策略，证明发送方Alice可100%成功作弊，推翻了原方案的安全性主张。

Insecurity of Quantum Bit Commitment with Secret Parameters

The impossibility proof of unconditionally secure quantum bit commitment is crucially dependent on the assertion that Bob is not allowed to generate probability distributions unknown to Alice. This assertion is actually not meaningful, because Bob can always cheat without being detected. In this paper we prove that, for any concealing protocol involving secret probability distributions, there exists a cheating unitary transformation that is known to Alice. Our result closes a gap in the original impossibility proof.

Unconditionally Secure Bit Commitment with Flying Qudits

In the task cryptographers call bit commitment, one party encrypts a prediction in a way that cannot be decrypted until they supply a key, but has only one valid key. Bit commitment has many applications, and has been much studied, but completely and provably secure schemes have remained elusive. Here we report a new development in physics-based cryptography which gives a completely new way of implementing bit commitment that is perfectly secure. The technique involves sending a quantum state (for instance one or more photons) at light speed in one of two or more directions, either along a sec…

使用无穷维系统的量子比特承诺光学实现

An optical implementation of quantum bit commitment using infinite-dimensional systems

针对以往认为无条件安全量子比特承诺不可能实现的问题，本研究提出基于Mach-Zehnder干涉仪的量子光学方法近似无穷维系统，可实现安全QBC的原理验证实验与实用方案，还能支撑其他多方密码协议并揭示基础物理关联。

Practical and unconditionally secure spacetime-constrained oblivious transfer

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…

Simplified quantum bit commitment using single photon nonlocality

We simplified our previously proposed quantum bit commitment (QBC) protocol based on the Mach-Zehnder interferometer, by replacing symmetric beam splitters with asymmetric ones. It eliminates the need for random sending time of the photons; thus, the feasibility and efficiency are both improved. The protocol is immune to the cheating strategy in the Mayers-Lo-Chau no-go theorem of unconditionally secure QBC, because the density matrices of the committed states do not satisfy a crucial condition on which the no-go theorem holds.

Practically secure quantum bit commitment based on quantum seals

The relationship between the quantum bit commitment (QBC) and quantum seal (QS) is studied. It is elaborated that QBC and QS are not equivalent, but QS protocols satisfying a stronger unconditional security requirement can lead to an unconditionally secure QBC. In this sense, QS is strictly stronger than QBC in security requirements. Based on an earlier proposal on sealing a single bit, a feasible QBC protocol is also put forward, which is secure in practice even if the cheater has a strong quantum computational power.

Coin Tossing is Strictly Weaker Than Bit Commitment

We define cryptographic assumptions applicable to two mistrustful parties who each control two or more separate secure sites between which special relativity guarantees a time lapse in communication. We show that, under these assumptions, unconditionally secure coin tossing can be carried out by exchanges of classical information. We show also, following Mayers, Lo and Chau, that unconditionally secure bit commitment cannot be carried out by finitely many exchanges of classical or quantum information. Finally we show that, under standard cryptographic assumptions, coin tossing is strictly weak…

Strong no-go theorem for Gaussian quantum bit commitment

Unconditionally secure bit commitment is forbidden by quantum mechanics. We extend this no-go theorem to continuous-variable protocols where both players are restricted to use Gaussian states and operations, which is a reasonable assumption in current-state optical implementations. Our Gaussian no-go theorem also provides a natural counter-example to a conjecture that quantum mechanics can be rederived from the assumption that key distribution is allowed while bit commitment is forbidden in Nature.

The quantum bit commitment theorem

Unconditionally secure two-party bit commitment based solely on the principles of quantum mechanics (without exploiting special relativistic signalling constraints, or principles of general relativity or thermodynamics) has been shown to be impossible, but the claim is repeatedly challenged. The quantum bit commitment theorem is reviewed here and the central conceptual point, that an `Einstein-Podolsky-Rosen' attack or cheating strategy can always be applied, is clarified. The question of whether following such a cheating strategy can ever be disadvantageous to the cheater is considered and an…

Why Quantum Bit Commitment And Ideal Quantum Coin Tossing Are Impossible

There had been well known claims of unconditionally secure quantum protocols for bit commitment. However, we, and independently Mayers, showed that all proposed quantum bit commitment schemes are, in principle, insecure because the sender, Alice, can almost always cheat successfully by using an Einstein-Podolsky-Rosen (EPR) type of attack and delaying her measurements. One might wonder if secure quantum bit commitment protocols exist at all. We answer this question by showing that the same type of attack by Alice will, in principle, break any bit commitment scheme. The cheating strategy genera…

Bit Commitment from Weak Non-Locality

So-called non-local boxes, which have been introduced as an idealization-in different respects-of the behavior of entangled quantum states, have been known to allow for unconditional bit commitment between the two involved parties. We show that, actually, any possible non-local correlation which produces random bits on both sides can be used to implement bit commitment, and that this holds even when the parties are allowed to delay their inputs to the box. Since a particular example is the behavior of an EPR pair, this resource allows for implementing unconditionally secure bit commitment as l…

Secure Quantum Bit Commitment Using Unstable Particles

Using unstable particles which decay by emitting neutrinos, we propose a quantum bit commitment protocol that is humanly impossible to break. Neutrinos carry away quantum information, but their interaction with matter is so weak that it would take an astronomically-sized machine just to catch them, not to mention performing controlled unitary operations on them. As a result quantum information is lost, and cheating is not possible even if the participants had access to the most powerful quantum computers that could ever be built. Therefore, for all practical purposes, our new protocol is as go…

Non-static Quantum Bit Commitment

Quantum bit commitment has been known to be impossible by the independent proofs of Mayers, and Lo and Chau, under the assumption that the whole quantum states right before the unveiling phase are static to users. We here provide an unconditionally secure non-static quantum bit commitment protocol with a trusted third party, which is not directly involved in any communications between users and can be limited not to get any information of commitment without being detected by users. We also prove that our quantum bit commitment protocol is not secure without the help of the trusted third party.…

基于可分离操作的诚实绑定量子比特承诺

Honest-binding quantum bit commitment from separable operations

通过限制承诺方仅执行可分离操作，实现了安全的量子比特承诺方案，并证明在此限制下，任何完美隐藏的比特承诺协议中，试图更改承诺的诚实承诺方将以高概率被检测到。

Bit Commitment from Non-Signaling Correlations

Central cryptographic functionalities such as encryption, authentication, or secure two-party computation cannot be realized in an information-theoretically secure way from scratch. This serves as a motivation to study what (possibly weak) primitives they can be based on. We consider as such starting points general two-party input-output systems that do not allow for message transmission, and show that they can be used for realizing unconditionally secure bit commitment as soon as they are non-trivial, i.e., cannot be securely realized from distributed randomness only.

Secret parameters in quantum bit commitment

The no-go theorem of unconditionally secure quantum bit commitment depends crucially on the assumption that Alice knows in detail all the probability distributions generated by Bob. We show that if a protocol is concealing, then the cheating unitary transformation is independent of any parameters (including probability distributions) secretly chosen by Bob, so that Alice can calculate it without knowing Bob's secret choices. Otherwise the protocol cannot be concealing. Our result shows that the original impossibility proof was based on an incorrect assumption, despite the fact that its conclus…

Security bound of cheat sensitive quantum bit commitment

Cheat sensitive quantum bit commitment (CSQBC) loosens the security requirement of quantum bit commitment (QBC), so that the existing impossibility proofs of unconditionally secure QBC can be evaded. But here we analyze the common features in all existing CSQBC protocols, and show that in any CSQBC having these features, the receiver can always learn a non-trivial amount of information on the sender's committed bit before it is unveiled, while his cheating can pass the security check with a probability not less than 50%. The sender's cheating is also studied. The optimal CSQBC protocols that c…

On the question of secret probability distributions in quantum bit commitment

The proof of the No-Go Theorem of unconditionally secure quantum bit commitment depends on the assumption that Alice knows every detail of the protocol, including the probability distributions associated with all the random variables generated by Bob. We argue that this condition may not be universally satisfied. In fact it can be shown that when Bob is allowed to use a secret probability distribution, the joint quantum state is inevitably mixed. It is then natural to ask if Alice can still cheat. A positive answer has been given by us [13] for the perfect concealing case. In this paper, we pr…

Secure quantum bit commitment against empty promises. II. The density matrix

We further study the security of the quantum bit commitment (QBC) protocol we previously proposed [Phys. Rev. A 74, 022332 (2006).], by analyzing the reduced density matrix ρ_{b}^{B} which describes the quantum state at Bob's side corresponding to Alice's committed bit b. It is shown that Alice will find ρ_{0}^{B}\perp ρ_{1}^{B} while the protocol remains concealing to Bob. On the contrary, the existing no-go theorem of unconditionally secure QBC is based on the condition ρ_{0}^{B}\simeq ρ_{1}^{B}. Thus the specific cheating strategy proposed in the no-go theorem does not necessarily applies t…

Cheat Sensitive Quantum Bit Commitment

We define cheat sensitive cryptographic protocols between mistrustful parties as protocols which guarantee that, if either cheats, the other has some nonzero probability of detecting the cheating. We give an example of an unconditionally secure cheat sensitive non-relativistic bit commitment protocol which uses quantum information to implement a task which is classically impossible; we also describe a simple relativistic protocol.

Quantum key distribution based on orthogonal states allows secure quantum bit commitment

For more than a decade, it was believed that unconditionally secure quantum bit commitment (QBC) is impossible. But basing on a previously proposed quantum key distribution scheme using orthogonal states, here we build a QBC protocol in which the density matrices of the quantum states encoding the commitment do not satisfy a crucial condition on which the no-go proofs of QBC are based. Thus the no-go proofs could be evaded. Our protocol is fault-tolerant and very feasible with currently available technology. It reopens the venue for other "post-cold-war" multi-party cryptographic protocols, e.…