Statistical Cryptography using a Fisher-Schrodinger Model

A principled procedure to infer a hierarchy of statistical distributions possessing ill-conditioned eigenstructures, from incomplete constraints, is presented. The inference process of the pdfs 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 pdfs 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 null spaces of the ill-conditioned eigenstructures, is presented. Numerical simulations exemplify the efficacy of the model