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 weaker than bit commitment. That is, no secure classical or quantum bit commitment protocol can be built from a finite number of invocations of a secure coin tossing black box together with finitely many additional information exchanges.
There had been well known claims of ``provably unbreakable'' quantum protocols for bit commitment and coin tossing. However, we, and independently Mayers, showed that all proposed quantum bit commitment (and therefore coin tossing) schemes are, in principle, insecure because the sender, Alice, can always cheat successfully by using an EPR-type of attack and delaying her measurements. One might wonder if secure quantum bit commitment and coin tossing protocols exist at all. Here we prove that an EPR-type of attack by Alice will, in principle, break {\em any} realistic quantum bit commitment and…
The relativistic quantum protocols realizing the bit commitment and distant coin tossing schemes are proposed. The protocols are based on the fact that the non-stationary orthogonal extended quantum states cannot be reliably distinguished if they are not fully accessible for the measurement. As the states propagate from the domain controlled by one of the user to the domain accessible for the measurements performed by the other user, they become reliably distinguishable for the second user. Important for the protocol are both the quantum nature of the states and the existence of a finite maxim…
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…
In the literature, strong coin tossing protocols based on bit commitment have been proposed. Here we examine a protocol that instead tries to achieve the task by sharing entanglement securely. The protocol uses only qubits, and has bias 1/4. This is equal to the best known bias for bit commitment based schemes.
We show that a secure quantum protocol for coin tossing exist. The existence of quantum coin tossing support the conjecture of D.Mayers [Phys.Rev.Lett. 78, 3414(1997)] that only asymmetrical tasks as quantum bit commitment are impossible.
We suggest an attack on a symmetric non-ideal quantum coin-tossing protocol suggested by Mayers Salvail and Chiba-Kohno. The analysis of the attack shows that the protocol is insecure.
A relativistic quantum information exchange protocol is proposed allowing two distant users to realize ``coin tossing'' procedure. The protocol is based on the point that in relativistic quantum theory reliable distinguishing between the two orthogonal states generally requires a finite time depending on the structure of these states.
We review the quantum version of a well known problem of cryptography called coin tossing (``flipping a coin via telephone''). It can be regarded as a game where two remote players (who distrust each other) tries to generate a uniformly distributed random bit which is common to both parties. The only resource they can use to perform this task is a classical or quantum communication channel. In this paper we provide a general overview over such coin tossing protocols, concerning in particular their security.
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.
A significant branch of classical cryptography deals with the problems which arise when mistrustful parties need to generate, process or exchange information. As Kilian showed a while ago, mistrustful classical cryptography can be founded on a single protocol, oblivious transfer, from which general secure multi-party computations can be built. The scope of mistrustful quantum cryptography is limited by no-go theorems, which rule out, inter alia, unconditionally secure quantum protocols for oblivious transfer or general secure two-party computations. These theorems apply even to protocols which…
In this letter we present the first implementation of a quantum coin tossing protocol. This protocol belongs to a class of ``two-party'' cryptographic problems, where the communication partners distrust each other. As with a number of such two-party protocols, the best implementation of the quantum coin tossing requires qutrits. In this way, we have also performed the first complete quantum communication protocol with qutrits. In our experiment the two partners succeeded to remotely toss a row of coins using photons entangled in the orbital angular momentum. We also show the experimental bound…
Alice is a charismatic quantum cryptographer who believes her parties are unmissable; Bob is a (relatively) glamorous string theorist who believes he is an indispensable guest. To prevent possibly traumatic collisions of self-perception and reality, their social code requires that decisions about invitation or acceptance be made via a cryptographically secure variable bias coin toss (VBCT). This generates a shared random bit by the toss of a coin whose bias is secretly chosen, within a stipulated range, by one of the parties; the other party learns only the random bit. Thus one party can secre…
The cryptographic protocol of coin tossing consists of two parties, Alice and Bob, that do not trust each other, but want to generate a random bit. If the parties use a classical communication channel and have unlimited computational resources, one of them can always cheat perfectly. Here we analyze in detail how the performance of a quantum coin tossing experiment should be compared to classical protocols, taking into account the inevitable experimental imperfections. We then report an all-optical fiber experiment in which a single coin is tossed whose randomness is higher than achievable by …
We discuss the security implications of noise for quantum coin tossing protocols. We find that if quantum error correction can be used, so that noise levels can be made arbitrarily small, then reasonable security conditions for coin tossing can be framed so that results from the noiseless case will continue to hold. If, however, error correction is not available (as is the case with present day technology), and significant noise is present, then tossing a single coin becomes problematic. In this case, we are led to consider random n-bit string generation in the presence of noise, rather than s…
In coin tossing two remote participants want to share a uniformly distributed random bit. At the least in the quantum version, each participant test whether or not the other has attempted to create a bias on this bit. It is requested that, for b = 0,1, the probability that Alice gets bit b and pass the test is smaller than 1/2 whatever she does, and similarly for Bob. If the bound 1/2 holds perfectly against any of the two participants, the task realised is called an exact coin tossing. If the bound is actually $1/2 + ξ$ where the bias $ξ$ vanishes when a security parameter m defined by the pr…
In extension of the bit commitment task and following work initiated by Crepeau and Kilian, we introduce and solve the problem of characterising the optimal rate at which a discrete memoryless channel can be used for bit commitment. It turns out that the answer is very intuitive: it is the maximum equivocation of the channel (after removing trivial redundancy), even when unlimited noiseless bidirectional side communication is allowed. By a well-known reduction, this result provides a lower bound on the channel's capacity for implementing coin tossing, which we conjecture to be an equality. The…
The security of quantum communication using a weak coherent source requires an accurate knowledge of the source's mean photon number. Finite calibration precision or an active manipulation by an attacker may cause the actual emitted photon number to deviate from the known value. We model effects of this deviation on the security of three quantum communication protocols: the Bennett-Brassard 1984 (BB84) quantum key distribution (QKD) protocol without decoy states, Scarani-Acin-Ribordy-Gisin 2004 (SARG04) QKD protocol, and a coin-tossing protocol. For QKD, we model both a strong attack using tec…
Quantum coin tossing (QCT) is an important primitive of quantum cryptography and has received continuous interest. However, in practical QCT, Bob's detectors can be subjected to detector-side channel attacks launched by dishonest Alice, which will possibly make the protocol completely insecure. Here, we report a simple strategy of a detector-blinding attack based on a recent experiment. To remove all the detector side channels, we present a solution of measurement-device-independent QCT (MDI-QCT). This method is similar to the idea of MDI quantum key distribution (QKD). MDI-QCT is loss toleran…
Joint Institute for Nuclear Research（联合核研究所）；Universidade de São Paulo（圣保罗大学）
The procedure of tossing quantum coins and dice is described. This case is an important example of a quantum procedure because it presents a typical framework employed in quantum information processing and quantum computing. The emphasis is on the clarification of the difference between quantum and classical conditional probabilities. These probabilities are designed for characterizing different systems, either quantum or classical, and they, generally, cannot be reduced to each other. Thus the Lüders probability cannot be treated as a generalization of the classical conditional probability. T…
It is well-known that pure quantum states are typically almost maximally entangled, and thus have close to maximally mixed subsystems. We consider whether this is true for probabilistic theories more generally, and not just for quantum theory. We derive a formula for the expected purity of a subsystem in any probabilistic theory for which this quantity is well-defined. It applies to typical entanglement in pure quantum states, coin tossing in classical probability theory, and randomization in post-quantum theories; a simple generalization yields the typical entanglement in (anti)symmetric quan…
When elementary quantum systems, such as polarized photons, are used to transmit digital information, the uncertainty principle gives rise to novel cryptographic phenomena unachievable with traditional transmission media, e.g. a communications channel on which it is impossible in principle to eavesdrop without a high probability of disturbing the transmission in such a way as to be detected. Such a quantum channel can be used in conjunction with ordinary insecure classical channels to distribute random key information between two users with the assurance that it remains unknown to anyone else,…
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 …
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.…
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…
We propose a coin-flip protocol which yields a string of strong, random coins and is fully simulatable against poly-sized quantum adversaries on both sides. It can be implemented with quantum-computational security without any set-up assumptions, since our construction only assumes mixed commitment schemes which we show how to construct in the given setting. We then show that the interactive generation of random coins at the beginning or during outer protocols allows for quantum-secure realizations of classical schemes, again without any set-up assumptions. As example applications we discuss q…
Coin tossing is a cryptographic task in which two parties who do not trust each other aim to generate a common random bit. Using classical communication this is impossible, but non trivial coin tossing is possible using quantum communication. Here we consider the case when the parties do not want to toss a single coin, but many. This is called bit string generation. We report the experimental generation of strings of coins which are provably more random than achievable using classical communication. The experiment is based on the ``plug and play'' scheme developed for quantum cryptography, and…
After a general introduction, the thesis is divided into four parts. In the first, we discuss the task of coin tossing, principally in order to highlight the effect different physical theories have on security in a straightforward manner, but, also, to introduce a new protocol for non-relativistic strong coin tossing. This protocol matches the security of the best protocol known to date while using a conceptually different approach to achieve the task. In the second part variable bias coin tossing is introduced. This is a variant of coin tossing in which one party secretly chooses one of two b…
Quantum protocols for coin-flipping can be composed in series in such a way that a cheating party gains no extra advantage from using entanglement between different rounds. This composition principle applies to coin-flipping protocols with cheat sensitivity as well, and is used to derive two results: There are no quantum strong coin-flipping protocols with cheat sensitivity that is linear in the bias (or bit-commitment protocols with linear cheat detection) because these can be composed to produce strong coin-flipping with arbitrarily small bias. On the other hand, it appears that quadratic ch…
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…
Relativistic protocols have been proposed to overcome some impossibility results in classical and quantum cryptography. In such a setting, one takes the location of honest players into account, and uses the fact that information cannot travel faster than the speed of light to limit the abilities of dishonest agents. For example, various relativistic bit commitment protocols have been proposed. Although it has been shown that bit commitment is sufficient to construct oblivious transfer and thus multiparty computation, composing specific relativistic protocols in this way is known to be insecure…
Robust and leakage-resilient device-independent oblivious transfer in MiniQCrypt
Centre for Quantum Technologies, Singapore（新加坡量子技术中心）；Department of Computer Science, National University of Singapore（新加坡国立大学计算机系）；MajuLab, UMI 3654, Singapore（新加坡UMI 3654 MajuLab）
We focus on a family of quantum coin-flipping protocols based on bit-commitment. We discuss how the semidefinite programming formulations of cheating strategies can be reduced to optimizing a linear combination of fidelity functions over a polytope. These turn out to be much simpler semidefinite programs which can be modelled using second-order cone programming problems. We then use these simplifications to construct their point games as developed by Kitaev. We also study the classical version of these protocols and use linear optimization to formulate optimal cheating strategies. We then cons…
We investigate sampling procedures that certify that an arbitrary quantum state on $n$ subsystems is close to an ideal mixed state $φ^{\otimes n}$ for a given reference state $φ$, up to errors on a few positions. This task makes no sense classically: it would correspond to certifying that a given bitstring was generated according to some desired probability distribution. However, in the quantum case, this is possible if one has access to a prover who can supply a purification of the mixed state. In this work, we introduce the concept of mixed-state certification, and we show that a natural sam…
A long sequence of tosses of a classical coin produces an apparently random bit string, but classical randomness is an illusion: the algorithmic information content of a classically-generated bit string lies almost entirely in the description of initial conditions. This letter presents a simple argument that, by contrast, a sequence of bits produced by tossing a quantum coin is, almost certainly, genuinely (algorithmically) random. This result can be interpreted as a strengthening of Bell's no-hidden-variables theorem, and relies on causality and quantum entanglement in a manner similar to Bel…
Methods of quantum mechanics promise information-theoretic security for various protocols in cryptography. However, impossibility of some cryptographic applications such as standard bit commitment, oblivious transfer, multiparty secure computations and ideal coin tossing in quantum regime leaves an obvious question on the completeness of quantum cryptography. Instead of using wide range of rules and techniques for a variety of cryptographic applications, we demonstrate here a unified structure for quantum cryptography based on quantum non-local correlations. The unified framework achieves same…
Unconditionally secure bit commitment and coin flipping are known to be impossible in the classical world. Bit commitment is known to be impossible also in the quantum world. We introduce a related new primitive - {\em quantum bit escrow}. In this primitive Alice commits to a bit $b$ to Bob. The commitment is {\em binding} in the sense that if Alice is asked to reveal the bit, Alice can not bias her commitment without having a good probability of being detected cheating. The commitment is {\em sealing} in the sense that if Bob learns information about the encoded bit, then if later on he is as…
A one way partial quantum bit commitment protocol is developed, using states with built-in classical correlation, completely independent of entanglement. It involves concealing information in a set of mutually non-orthogonal states and revealing it through measurements on a set of product states that are mutually orthogonal. Given $2^N$ choices to commit from, the protocol encodes each choice in a $N+1$ qubit state, from $2^N$ non-orthogonal states. A previously agreed upon $N$ qubit state corresponding to each choice, when coupled with the $N+1$ qubit state, yields an element belonging to a s…
Bit commitment and coin flipping occupy a unique place in the device-independent landscape, as the only device-independent protocols thus far suggested for these tasks are reliant on tripartite GHZ correlations. Indeed, we know of no other bipartite tasks, which admit a device-independent formulation, but which are not known to be implementable using only bipartite nonlocality. Another interesting feature of these protocols is that the pseudo-telepathic nature of GHZ correlations -- in contrast to the generally statistical character of nonlocal correlations, such as those arising in the violat…
We consider the cryptographic task of bit-string generation. This is a generalisation of coin tossing in which two mistrustful parties wish to generate a string of random bits such that an honest party can be sure that the other cannot have biased the string too much. We consider a quantum protocol for this task, originally introduced in Phys. Rev. A {\bf 69}, 022322 (2004), that is feasible with present day technology. We introduce security conditions based on the average bias of the bits and the Shannon entropy of the string. For each, we prove rigorous security bounds for this protocol in b…
