A Spin Glass Model for Reconstructing Nonlinearly Encrypted Signals Corrupted by Noise

摘要

We define a (symmetric key) encryption of a signal sRN as a random mapping s?y=(y1,...,yM)TRM known both to the sender and a recipient. In general the recipients may have access only to images y corrupted by an additive noise of unknown strength. Given the encryption redundancy parameter (ERP) =M/N1 and the signal strength parameter R=0 for any >1 and any <, with p approximate to-1/2 as . In contrast, for the case of purely quadratic nonlinearity, for any ERP >1 there exists a threshold NSR value c() such that p=0 for >c() making the reconstruction impossible. The behaviour close to the threshold is given by p approximate to 3/4 and is controlled by the replica symmetry breaking mechanism.