Random-Energy Secret Sharing via Extreme Synergy

TL;DR

This paper introduces a secret-sharing scheme based on the random-energy model (REM), demonstrating its security properties and optimality in information encoding through analytical and numerical analysis.

Contribution

It establishes a novel connection between REM and secret sharing, analyzing its information-theoretic security and identifying conditions for optimal secret encoding.

Findings

REM correlations enable secure secret sharing

Optimal secret encoding occurs at a specific phase diagram point

Numerical simulations support analytical thermodynamic limit results

Abstract

The random-energy model (REM), a solvable spin-glass model, has impacted an incredibly diverse set of problems, from protein folding to combinatorial optimization to many-body localization. Here, we explore a new connection to secret sharing. We formulate a secret-sharing scheme, based on the REM, and analyze its information-theoretic properties. Our analyses reveal that the correlations between subsystems of the REM are highly synergistic and form the basis for secure secret-sharing schemes. We derive the ranges of temperatures and secret lengths over which the REM satisfies the requirement of secure secret sharing. We show further that a special point in the phase diagram exists at which the REM-based scheme is optimal in its information encoding. Our analytical results for the thermodynamic limit are in good qualitative agreement with numerical simulations of finite systems, for which the strict security requirement is replaced by a tradeoff between secrecy and recoverability. Our work offers a further example of information theory as a unifying concept, connecting problems in statistical physics to those in computation.