[Paper Review] The physics of no-bit-commitment : Generalized quantum non-locality versus oblivious transfer

Tony Short, Nicolas Gisin+1 more|ArXiv.org|Apr 18, 2005

Quantum and electron transport phenomena5 citations

TL;DR

This paper resolves a paradox in quantum foundations by showing that while PR-boxes (stronger-than-quantum non-local correlations) can simulate oblivious transfer, they cannot enable secure bit-commitment due to the lack of time-ordering constraints on inputs. Unlike oblivious transfer, PR-boxes allow Alice to delay her measurement until the reveal phase, violating the binding condition and undermining security, thus highlighting that non-signaling alone is insufficient for bit-commitment—timing of inputs is essential.

ABSTRACT

We show here that the recent work of Wolf and Wullschleger (quant-ph/0502030) on oblivious transfer apparently opens the possibility that non-local correlations which are stronger than those in quantum mechanics could be used for bit-commitment. This is surprising, because it is the very existence of non-local correlations which in quantum mechanics prevents bit-commitment. We resolve this apparent paradox by stressing the difference between non-local correlations and oblivious transfer, based on the time-ordering of their inputs and outputs, which prevents bit-commitment.

Motivation & Objective

• To resolve the apparent contradiction that PR-boxes—stronger than quantum non-local correlations—could enable bit-commitment, despite quantum mechanics forbidding it.
• To clarify why PR-boxes, despite simulating oblivious transfer, cannot implement secure bit-commitment.
• To emphasize the critical role of input timing order in distinguishing secure cryptographic primitives from non-local correlations.
• To demonstrate that non-signaling alone does not guarantee security in bit-commitment, even when correlations are stronger than quantum ones.

Proposed method

• Constructing a bit-commitment protocol using OT-boxes (oblivious transfer boxes) to show it satisfies correctness, privacy, and secure binding.
• Simulating OT-box outputs using PR-boxes and classical communication to create an analogous protocol with PR-boxes.
• Analyzing the timing of inputs and outputs in the PR-box-based protocol, showing Alice can delay her inputs until the reveal phase.
• Demonstrating that Alice can cheat with certainty by choosing her bit after the COMMIT phase, violating the binding condition.
• Using the fact that PR-boxes are non-signaling and produce outputs regardless of input order, to show no detection of cheating is possible during COMMIT.
• Comparing the dynamics of OT-boxes (where Bob sees inputs only after Alice's) with PR-boxes (where outputs are independent of input order), highlighting the structural difference.

Experimental results

Research questions

• RQ1 Can PR-boxes, which simulate oblivious transfer, be used to implement secure bit-commitment?
• RQ2 Why does the simulation of OT-boxes by PR-boxes fail to preserve the security of bit-commitment protocols?
• RQ3 What role does the time-ordering of inputs play in preventing cheating in bit-commitment schemes?
• RQ4 Is non-locality alone sufficient for secure bit-commitment, or are additional constraints required?
• RQ5 Can any non-signaling non-local correlation box enable bit-commitment if input timing is unconstrained?

Key findings

• The protocol using OT-boxes satisfies correctness, privacy, and secure binding, making it a secure bit-commitment scheme.
• The analogous protocol using PR-boxes fails to be binding because Alice can delay her measurement until the reveal phase, allowing her to cheat with certainty.
• The crucial difference lies in input timing: OT-boxes require Alice to input her data before Bob, while PR-boxes produce outputs regardless of input order.
• Even with multiple PR-boxes in parallel, Alice can cheat independently on each, maintaining a 100% success rate.
• The non-signaling nature of PR-boxes, while preventing superluminal signaling, enables Alice to postpone her measurement, undermining the binding condition.
• The result implies that non-signaling alone is insufficient for bit-commitment; the dynamics of input timing are essential for security.