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.
This article describes a quantum bit commitment protocol, QBC1, based on entanglement destruction via forced measurements and proves its unconditional security.
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.
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.
This paper has been withdrawn by the authors,because the proposed protocol is still coverd by the no-go theorem of Mayers, Lo and Chau.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.
The ``impossibility proof'' on unconditionally secure quantum bit commitment is examined. It is shown that the possibility of juxtaposing quantum and classical randomness has not been properly taken into account. A specific protocol that beats entanglement cheating with entanglement is proven to be unconditionally secure.
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.
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…
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…
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.
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…
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…
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…
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…
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.
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…
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…
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…
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 (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…
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…
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…
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…
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.
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.
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…
A quantum protocol for bit commitment the security of which is based on technological limitations on nondemolition measurements and long-term quantum memory is presented.
We propose a framework of bit commitment protocol using a comparison scheme and present a compound comparison scheme based on counterfactual cryptography. Finally, we propose a counterfactual quantum bit commitment protocol. In security analysis, we give the proper security parameters for counterfactual quantum bit commitment and prove that intercept attack and intercept/resend attack are ineffective attack for our protocol. In addition, we explain that counterfactual quantum bit commitment protocol cannot be attacked with no-go theorem attack by current technology.
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.
We propose here a two-round relativistic bit commitment scheme where committer commits in the first round and then confirms his/her commitment in the second round. The scheme offers indefinite commitment time where both committer and receiver extract non-locally correlated measurement outcomes during the scheme that can be stored and revealed after arbitrarily long time. We show that the proposed scheme turns out to be a multiparty bit commitment scheme where both parties commit and reveal simultaneously. The multiparty generalization would have applications in business and secure multiparty c…
In this paper, we introduce a new quantum bit commitment protocol which is practically secure against entanglement attacks. A general cheating strategy is discussed and shown to be practically ineffective against the proposed approach.
This paper considers the use an entanglement breaking channel in the construction of a secure bit-commitment protocol. It is shown that this can be done via a depolarizing quantum channel.
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…
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…
The impossibility proof on unconditionally secure quantum bit commitment is critically reviewed. Different ways of obtaining secure protocols are indicated.
Under rather general assumptions about the properties of a noisy quantum channel, a first quantum protocol is proposed which allows to implement the secret bit commitment with the probability arbitrarily close to unity.
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.
In this work, we propose a quantum bit string commitment protocol using polarization of mesoscopic coherent states. The protocol is described and its security against brute force and quantum cloning machine attack is analyzed.
We propose a practical quantum oblivious transfer and a bit commitment protocols which replace the single-photon source with weak coherent pulses and allow error and loss in channel and detectors. These protocols can be realized with available optoelectronic apparatus.
This paper proposes a cheat sensitive quantum bit commitment (CSQBC) scheme based on single photons, in which Alice commits a bit to Bob. Here, Bob only can cheat the committed bit with probability close to $0$ with the increasing of used single photons' amount. And if Alice altered her committed bit after commitment phase, she will be detected with probability close to $1$ with the increasing of used single photons' amount. The scheme is easy to be realized with nowadays technology.
The nature and scope of various impossibility proofs as they relate to real-world situations are discussed. In particular, it is shown in words without technical symbols how secure quantum bit commitment protocols may be obtained with testing that exploits the multiple possibilities of cheating entanglement formation.
We show here that the recent work of Wolf and Wullschleger (quant-ph/0502030) on oblivious transfer apparently opens the possibility that non-local correlations which are stronger than those in quantum mechanics could be used for bit-commitment. This is surprising, because it is the very existence of non-local correlations which in quantum mechanics prevents bit-commitment. We resolve this apparent paradox by stressing the difference between non-local correlations and oblivious transfer, based on the time-ordering of their inputs and outputs, which prevents bit-commitment.
The aim of this thesis project is to investigate the bit commitment protocol in the framework of operational probabilistic theories. In particular a careful study is carried on the feasibility of bit commitment in the non-local boxes theory. New aspects of the theory are also presented.
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 …
Several kinds of qubit-string-based(QS-based) bit commitment protocols are presented, and a definition of information-theoretic concealing is given. All the protocols presented here are proved to be secure under this definition. We suggest an attack algorithm to obtain the local unitary transformation introduced in no-go theorem, which is used to attack the binding condition, then study the security of our QS-based bit commitment protocols under this attack via introducing a new concept "physical security of protocol". At last we present a practical QS-based bit commitment scheme against chann…
We provide a non-interactive quantum bit commitment scheme which has statistically-hiding and computationally-binding properties from any quantum one-way function. Our protocol is basically a parallel composition of the previous non-interactive quantum bit commitment schemes (based on quantum one-way permutations, due to Dumais, Mayers and Salvail (EUROCRYPT 2000)) with pairwise independent hash functions. To construct our non-interactive quantum bit commitment scheme from any quantum one-way function, we follow the procedure below: (i) from Dumais-Mayers-Salvail scheme to a weakly-hiding and …
Bit commitment is a fundamental cryptographic primitive with numerous applications. Quantum information allows for bit commitment schemes in the information theoretic setting where no dishonest party can perfectly cheat. The previously best-known quantum protocol by Ambainis achieved a cheating probability of at most 3/4[Amb01]. On the other hand, Kitaev showed that no quantum protocol can have cheating probability less than 1/sqrt{2} [Kit03] (his lower bound on coin flipping can be easily extended to bit commitment). Closing this gap has since been an important and open question. In this pape…
We investigate the existence of secure bit commitment protocols in the convex framework for probabilistic theories. The framework makes only minimal assumptions, and can be used to formalize quantum theory, classical probability theory, and a host of other possibilities. We prove that in all such theories that are locally non-classical but do not have entanglement, there exists a bit commitment protocol that is exponentially secure in the number of systems used.
In a recent letter (Phys. Lett. A 377 (2013) 1076, arXiv:0905.3801), the authors presented an impossibility proof of quantum bit commitment, which attempted to cover all possible protocols that involve both quantum and classical information. Here we show that there are many errors in the proof, thus it fails to exhaust all conceivable protocols.
We proposed a new quantum bit commitment scheme in which secret key need not to be provided by other quantum key distribution system. We can get the bit commitment with probability p by adding a waiting time in a frame during operating the BB84 protocol. Then the measurement outcomes can be encrypted by one-time pad with the key generated by BB84 protocol. We can also obtain the redundant secret keys to encrypt other information in this quantum key distribution system.
