Statistical Cryptography using a Fisher-Schr\"{o}dinger Model

TL;DR

This paper introduces a novel statistical cryptography framework based on Fisher-Schrödinger models, inferring complex distributions from incomplete data and enabling secure encryption through quantum-inspired null space projections.

Contribution

It presents a new method combining Fisher information and quantum mechanics concepts to infer distributions and perform secure encryption with ill-conditioned eigenstructures.

Findings

Effective encryption/decryption demonstrated via numerical simulations

Hierarchical distributions inferred from incomplete constraints

Quantum mechanical interpretation enhances statistical inference

Abstract

A principled procedure to infer a hierarchy of statistical distributions possessing ill-conditioned eigenstructures, from incomplete constraints, is presented. The inference process of the \textit{pdf}'s employs the Fisher information as the measure of uncertainty, and, utilizes a semi-supervised learning paradigm based on a measurement-response model. The principle underlying the learning paradigm involves providing a quantum mechanical connotation to statistical processes. The inferred \textit{pdf}'s constitute a statistical host that facilitates the encryption/decryption of covert information (code). A systematic strategy to encrypt/decrypt code via unitary projections into the \textit{null spaces} of the ill-conditioned eigenstructures, is presented. Numerical simulations exemplify the efficacy of the model.