Brief History of Quantum Cryptography: A Personal Perspective

Quantum cryptography is the only approach to privacy ever proposed that allows two parties (who do not share a long secret key ahead of time) to communicate with provably perfect secrecy under the nose of an eavesdropper endowed with unlimited computational power and whose technology is limited by nothing but the fundamental laws of nature. This essay provides a personal historical perspective on the field. For the sake of liveliness, the style is purposely that of a spontaneous after-dinner speech.Comment: 14 pages, no figure

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 generally requires a quantum computer. We emphasize the generality of this ``no-go theorem'': Unconditionally secure bit commitment schemes based on quantum mechanics---fully quantum, classical or quantum but with measurements---are all ruled out by this result. Since bit commitment is a useful primitive for building up more sophisticated protocols such as zero-knowledge proofs, our results cast very serious doubt on the security of quantum cryptography in the so-called ``post-cold-war'' applications. We also show that ideal quantum coin tossing is impossible because of the EPR attack. This no-go theorem for ideal quantum coin tossing may help to shed some lights on the possibility of non-ideal protocols.Comment: We emphasize the generality of this "no-go theorem". All bit commitment schemes---fully quantum, classical and quantum but with measurements---are shown to be necessarily insecure. Accepted for publication in a special issue of Physica D. About 18 pages in elsart.sty. This is an extended version of an earlier manuscript (quant-ph/9605026) which has appeared in the proceedings of PHYSCOMP'9

Experimental quantum tossing of a single coin

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 any classical protocol and present some easily realisable cheating strategies by Alice and Bob.Comment: 13 page

A proposal for founding mistrustful quantum cryptography on coin tossing

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 take relativistic signalling constraints into account. The best that can be hoped for, in general, are quantum protocols computationally secure against quantum attack. I describe here a method for building a classically certified bit commitment, and hence every other mistrustful cryptographic task, from a secure coin tossing protocol. No security proof is attempted, but I sketch reasons why these protocols might resist quantum computational attack.Comment: Title altered in deference to Physical Review's fear of question marks. Published version; references update

Experimental Quantum Coin Tossing

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 bounds of a possible cheater and the ways of detecting him

Quantum Bit Commitment with a Composite Evidence

Entanglement-based attacks, which are subtle and powerful, are usually believed to render quantum bit commitment insecure. We point out that the no-go argument leading to this view implicitly assumes the evidence-of-commitment to be a monolithic quantum system. We argue that more general evidence structures, allowing for a composite, hybrid (classical-quantum) evidence, conduce to improved security. In particular, we present and prove the security of the following protocol: Bob sends Alice an anonymous state. She inscribes her commitment $b$ by measuring part of it in the + (for $b = 0$) or $\times$ (for $b=1$) basis. She then communicates to him the (classical) measurement outcome $R_x$ and the part-measured anonymous state interpolated into other, randomly prepared qubits as her evidence-of-commitment.Comment: 6 pages, minor changes, journal reference adde

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 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.Comment: Final version; to appear in Phys. Rev. Let

Quantum Gambling Using Three Nonorthogonal States

We provide a quantum gambling protocol using three (symmetric) nonorthogonal states. The bias of the proposed protocol is less than that of previous ones, making it more practical. We show that the proposed scheme is secure against non-entanglement attacks. The security of the proposed scheme against entanglement attacks is shown heuristically.Comment: no essential correction, 4 pages, RevTe