A bit string commitment protocol securely commits $N$ classical bits in such a way that the recipient can extract only $M<N$ bits of information about the string. Classical reasoning might suggest that bit string commitment implies bit commitment and hence, given the Mayers-Lo-Chau theorem, that non-relativistic quantum bit string commitment is impossible. Not so: there exist non-relativistic quantum bit string commitment protocols, with security parameters $ε$ and $M$, that allow $A$ to commit $N = N(M, ε)$ bits to $B$ so that $A$'s probability of successfully cheating when revealing any bit and $B$'s probability of extracting more than $N'=N-M$ bits of information about the $N$ bit string before revelation are both less than $ε$. With a slightly weakened but still restrictive definition of security against $A$, $N$ can be taken to be $O(\exp (C N'))$ for a positive constant $C$. I briefly discuss possible applications.
Oblivious transfer protocols (R-OT and OT$_{1}^{2}$) are presented based on non-orthogonal states transmission, and the bit commitment protocols on the top of OT$_{1}^{2}$ are constructed. Although these OT protocols are all unconditional secure, the bit commitment protocols based on OT protocols are not secure against attack similar to that presented by no-go theorem.
We examine the possibility of device-independent relativistic quantum bit commitment. We note the potential threat of {\it location attacks}, in which the behaviour of untrusted devices used in relativistic quantum cryptography depends on their space-time location. We describe relativistic quantum bit commitment schemes that are immune to these attacks, and show that these schemes offer device-independent security against hypothetical post-quantum adversaries subject only to the no-signalling principle. We compare a relativistic classical bit commitment scheme with similar features, and note s…
We present a new quantum bit commitment (QBC) protocol based on counterfactual quantum cryptography. We analyze the security of this protocol, find that it can resist the attack presented by QBC's no-go theorem. Our protocol is simple, and probably give a new way of constructing QBC protocol.
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…
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…
We show that all proposed quantum bit commitment schemes are insecure because the sender, Alice, can almost always cheat successfully by using an Einstein-Podolsky-Rosen type of attack and delaying her measurement until she opens her 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.
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…
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.
We describe new unconditionally secure bit commitment schemes whose security is based on Minkowski causality and the monogamy of quantum entanglement. We first describe an ideal scheme that is purely deterministic, in the sense that neither party needs to generate any secret randomness at any stage. We also describe a variant that allows the committer to proceed deterministically, requires only local randomness generation from the receiver, and allows the commitment to be verified in the neighbourhood of the unveiling point. We show that these schemes still offer near-perfect security in the p…
We consider the recent relativistic bit commitment protocol introduced by Lunghi et al. [Phys. Rev. Lett. 2015] and present a new security analysis against classical attacks. In particular, while the initial complexity of the protocol scaled double-exponentially with the commitment time, our analysis shows that the correct dependence is only linear. This has dramatic implications in terms of implementation: in particular, the commitment time can easily be made arbitrarily long, by only requiring both parties to communicate classically and perform efficient classical computation.
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 …
We propose an entanglement-based quantum bit string commitment protocol whose composability is proven in the random oracle model. This protocol has the additional property of preserving the privacy of the committed message. Even though this property is not resilient against man-in-the-middle attacks, this threat can be circumvented by considering that the parties communicate through an authenticated channel. The protocol remains secure (but not private) if we realize the random oracles as physical unclonable functions in the so-called bad PUF model with access before the opening phase.
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.
It is well known that unconditionally secure bit commitment is impossible even in the quantum world. In this paper a weak variant of quantum bit commitment, introduced independently by Aharonov et al. [STOC, 2000] and Hardy and Kent [Phys. Rev. Lett. 92 (2004)] is investigated. In this variant, the parties require some nonzero probability of detecting a cheating, i.e. if Bob, who commits a bit b to Alice, changes his mind during the revealing phase then Alice detects the cheating with a positive probability (we call this property binding); and if Alice gains information about the committed bit…
This article describes a quantum bit commitment protocol, QBC1, based on entanglement destruction via forced measurements and proves its unconditional security.
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.
Relativistic cryptography exploits the fact that no information can travel faster than the speed of light in order to obtain security guarantees that cannot be achieved from the laws of quantum mechanics alone. Recently, Lunghi et al [Phys. Rev. Lett. 2015] presented a bit commitment scheme where each party uses two agents that exchange classical information in a synchronized fashion, and that is both hiding and binding. A caveat is that the commitment time is intrinsically limited by the spatial configuration of the players, and increasing this time requires the agents to exchange messages du…
Recently, Choi \emph{et al}. proposed an assumption on Mayers-Lo-Chau (MLC) no-go theorem that the state of the entire quantum system is invariable to both participants before the unveiling phase. This means that the theorem is only applicable to static quantum bit commitment (QBC). This paper find that the assumption is unnecessary and the MLC no-go theorem can be applied to not only static QBC, but also non-static one. A non-static QBC protocol proposed by Choi \emph{et al.} is briefly reviewed and analyzed to work as a supporting example. In addition, a novel way to prove the impossibility …
In this paper, we focus on a special framework for quantum coin flipping protocols,_bit-commitment based protocols_, within which almost all known protocols fit. We show a lower bound of 1/16 for the bias in any such protocol. We also analyse a sequence of multi-round protocol that tries to overcome the drawbacks of the previously proposed protocols, in order to lower the bias. We show an intricate cheating strategy for this sequence, which leads to a bias of 1/4. This indicates that a bias of 1/4 might be optimal in such protocols, and also demonstrates that a cleverer proof technique may be …
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…
If mutually mistrustful parties A and B control two or more appropriately located sites, special relativity can be used to guarantee that a pair of messages exchanged by A and B are independent. In earlier work, we used this fact to define a relativistic bit commitment protocol, RBC1, in which security is maintained by exchanging a sequence of messages whose transmission rate increases exponentially in time. We define here a new relativistic protocol, RBC2, which requires only a constant transmission rate and could be practically implemented. We prove that RBC2 allows a bit commitment to be in…
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…
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.
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.
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.
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.
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.
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…
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.
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…
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.
Quantum bit-string commitment[A.Kent, Phys.Rev.Lett., 90, 237901 (2003)] or QBSC is a variant of bit commitment (BC). In this paper, we propose a new QBSC protocol that can be implemented using currently available technology, and prove its security under the same security criteria as discussed by Kent. QBSC is a generalization of BC, but has slightly weaker requirements, and our proposed protocol is not intended to break the no-go theorem of quantum BC.
We introduce a new setting for two-party cryptography with temporarily trusted third parties. In addition to Alice and Bob in this setting, there are additional third parties, which Alice and Bob both trust to be honest during the protocol. However, once the protocol concludes, there is no guarantee over the behaviour of these third parties. It is possible that they collaborate and act adversarially. Our goal is to use these third parties to facilitate protocols which are impossible in two-party cryptography. We implement a variant of bit commitment in this setting, which we call erasable bit …
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.…
Bit-commitment is a fundamental cryptographic task, in which Alice commits a bit to Bob such that she cannot later change the value of the bit, while, simultaneously, the bit is hidden from Bob. It is known that ideal bit-commitment is impossible within quantum theory. In this work, we show that it is also impossible in generalised probabilistic theories (under a small set of assumptions) by presenting a quantitative trade-off between Alice's and Bob's cheating probabilities. Our proof relies crucially on a formulation of cheating strategies as cone programs, a natural generalisation of semide…
Quantum bit commitment has long been known to be impossible. Nevertheless, just as in the classical case, imposing certain constraints on the power of the parties may enable the construction of asymptotically secure protocols. Here, we introduce a quantum bit commitment protocol and prove that it is asymptotically secure if cheating is restricted to Gaussian operations. This protocol exploits continuous-variable quantum optical carriers, for which such a Gaussian constraint is experimentally relevant as the high optical nonlinearity needed to effect deterministic non-Gaussian cheating is inacc…
