Degrees of concealment and bindingness in quantum bit commitment protocols

Abstract

Although it is impossible for a bit commitment protocol to be both arbitrarily concealing and arbitrarily binding, it is possible for it to be both partially concealing and partially binding. This means that Bob cannot, prior to the beginning of the unveiling phase, find out everything about the bit committed, and Alice cannot, through actions taken after the end of the commitment phase, unveil whatever bit she desires. We determine upper bounds on the degrees of concealment and bindingness that can be achieved simultaneously in any bit commitment protocol, although it is unknown whether these can be saturated. We do, however, determine the maxima of these quantities in a restricted class of bit commitment protocols, namely those wherein all the systems that play a role in the commitment phase are supplied by Alice. We show that these maxima can be achieved using a protocol that requires Alice to prepare a pair of systems in an entangled state, submit one of the pair to Bob at the commitment phase, and the other at the unveiling phase. Finally, we determine the form of the trade-off that exists between the degree of concealment and the degree of bindingness given various assumptions about the purity and dimensionality of the states used in the protocol.

Variable-bias coin tossing

“…The discoveries of quantum cryptography [1] and provably secure quantum key distribution [2,3,4,5,6] motivated a general search for protocols which implement interesting cryptographic tasks in a way that can be guaranteed secure by quantum theory (for example [7,8,9,10,11,12,13,14,15,16,17]), by the impossibility of superluminal signalling [18,19,20], or both. The full cryptographic power of these physical principles is presently unknown: ideally, one would like to generate either a provably secure protocol or a no-go theorem for every interesting task.…”

Measuring Entangled Qutrits and Their Use for Quantum Bit Commitment

“…PACS numbers: 42.50.Dv, 03.65.Wj, 03.67.Dd, 03.67.Mn Many two-level quantum systems, or qubits, have been used to encode information [1]; using d-level systems, or qudits, enables access to larger Hilbert spaces, which can provide significant improvements over qubits such as increased channel capacity in quantum communication [2]. When entangled, qutrits (d=3) provide the best known levels of security in quantum bit-commitment and coinflipping protocols, which cannot be matched using qubitbased systems [3]. The ability to completely characterise entangled qudits is critical for applications.…”

Quantum Walks with Encrypted Data

“…As Bob simply performs his secret operation upon Alice's input and returns it to her, the information Alice obtains is exactly the same as if she makes a single query to a black box function, and so Alice obtains the minimum possible information about Bob's secret unitary. The probability of Bob correctly determining Alice's input is substantially higher than the exponentially small bound one may hope for, but such a strong bound would violate the no-go theorems for oblivious transfer and bit commitment [27,28]. An alternate approach for Alice is to run many computations with different input states, where only one is her desired state and the remainder are dummies.…”