Secure bit commitment from relativistic constraints

TL;DR

This paper explores secure bit commitment protocols leveraging relativistic no-signalling constraints and quantum mechanics, identifying minimal split models for security and proving the security of Kent's protocol under these physical principles.

Contribution

It introduces minimal split models necessary for secure bit commitment and provides a rigorous security proof for Kent's quantum protocol using physics principles.

Findings

Classical protocols are insecure under global command in split models.

Security is achievable in quantum protocols using no-signalling and uncertainty principles.

Minimal splits necessary to evade no-go theorems are characterized.

Abstract

We investigate two-party cryptographic protocols that are secure under assumptions motivated by physics, namely relativistic assumptions (no-signalling) and quantum mechanics. In particular, we discuss the security of bit commitment in so-called split models, i.e. models in which at least some of the parties are not allowed to communicate during certain phases of the protocol. We find the minimal splits that are necessary to evade the Mayers-Lo-Chau no-go argument and present protocols that achieve security in these split models. Furthermore, we introduce the notion of local versus global command, a subtle issue that arises when the split committer is required to delegate non-communicating agents to open the commitment. We argue that classical protocols are insecure under global command in the split model we consider. On the other hand, we provide a rigorous security proof in the global command model for Kent's quantum protocol [Kent 2011, Unconditionally Secure Bit Commitment by Transmitting Measurement Outcomes]. The proof employs two fundamental principles of modern physics, the no-signalling property of relativity and the uncertainty principle of quantum mechanics.