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

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.