String commitment from unstructured noise

TL;DR

This paper introduces the unstructured noisy channel model, a generalization allowing adversaries to arbitrarily manipulate channels within entropic limits, and presents a secure string commitment protocol under this model.

Contribution

It extends the noisy channel framework to a more powerful adversarial model and links it to physical assumptions like noisy quantum storage.

Findings

Secure string commitment protocol with established security

Achievable commitment rate derived for the unstructured noisy channel

Connection between entropic constraints and physical assumptions like quantum storage

Abstract

Noisy channels are a foundational resource for constructing cryptographic primitives such as string commitment and oblivious transfer. The noisy channel model has been extended to unfair noisy channels, where adversaries can influence the parameters of a memoryless channel. In this work, we introduce the unstructured noisy channel model as a generalization of the unfair noisy channel model to allow the adversary to manipulate the channel arbitrarily subject to certain entropic constraints. We present a string commitment protocol with established security and derive its achievable commitment rate, demonstrating the feasibility of commitment against this stronger class of adversaries. Furthermore, we show that the entropic constraints in the unstructured noisy channel model can be derived from physical assumptions such as noisy quantum storage. Our work thus connects two distinct approaches to commitment, i.e., the noisy channel and physical limitations.