Quantum one-time tables for unconditionally secure qubit-commitment

Abstract

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 in the standard model, based on the consumption of the quantum generalization of the OTT, the bipartite quantum state we named quantum one-time tables (QOTT). The construction of the QOTT is based on the newly analyzed internal structure of quantum masker and the quantum secret sharing schemes. Our qubit-commitment scheme is shown to be universally composable. We propose to measure the randomness cost of preparing a (Q)OTT in terms of its entropy, and show that the QOTT with superdense coding can increase the security level with half the cost of OTTs for unconditionally secure bit-commitment. The QOTT exemplifies an operational setting where neither maximally classically correlated state nor maximally entangled state, but rather a well-structured partially entangled mixed state is more valuable resource.

Unconditionally Secure Relativistic Quantum Qubit Commitment

“…Quantum qubit commitment is a rather new concept, which was first proposed in 2018 [14]. It was pointed out in 2021 [15] that the quantum qubit commitment has some unique and important applications beyond quantum bit commitment in the upcoming era of quantum network. Therefore, it is both theoretically interesting and practically valuable to develop unconditional secure quantum qubit commitment protocols.…”

“…It was found that the quantum qubit commitment has some unique applications [15] beyond quantum bit commitment in the upcoming era of quantum network, including implementing a fair version of quantum state exchange [16] and preventing cheating in such a task that two quantum computers are demanded to generate certain quantum states independently and to be cross-checked afterward [17], in which one computer may try to delay to generate its state after the other party and cheat by learning from the other party's state or even try to imperfectly clone the state to pretend to have high computational power. It was also pointed out [15] that secure quantum qubit commitment can break asynchronous quantum network assumption since it can effectively activate multiple quantum machines at the same time. These unique applications motivate the wide range of interest of developing unconditional security quantum qubit commitment protocols.…”

“…In Ref. [15], a secure quantum qubit commitment scheme is proposed by using the approach of quantum one-time tables, in which a trusted third party is needed. To the best of our knowledge, however, it remains an open question whether unconditionally secure quantum qubit commitment protocol can be realized in relativistic domain.…”

“…In Ref. [15], the authors defined that a quantum qubit commitment scheme is unconditionally secure if, without any assumption on computational power, its output is indistinguishable from the output of an instance of the ideal functionality unless the probability of the committer passing the unveil phase is lower than a certain threshold which can be made arbitrarily small by increasing the security parameters. Here we give a more straightforward mathematical description as: a quantum qubit commitment scheme is unconditionally secure if it guarantees ∑ k p k < 1 + δ(N) with δ(N) → 0 as N → ∞ , where N is the security parameter and p k is the probability of successfully unveiling the kth qubit of the qubit set in the unveil phase.…”

Delocalized and dynamical catalytic randomness and information flow

“…Hence, in a sense, forgetting information could create randomness. Thus, an archetype of such resource theory is the resource theory of randomness (RTR) [15][16][17][18][19] based on the theory of catalytic quantum randomness of Boes et al [20]. In the RTR, pure states are considered free and unitary operations are free operations, but none of them have convex structure.…”