Large deviations for performance analysis of signature authentication

In signature authentication schemes, a noisy measurement of a signature is used as a template against which a noisy measurement of a candidate signature is compared for authenticity. The signatures are modeled as realizations of a random process with known statistics. Stein's lemma may be used to determine the rate function for the probability of missed detection for an optimal detector. We consider in detail the special case where the signature and the noise are zero mean stationary Gaussian random processes. We find the rate function parameterized by the power spectra of the processes. These results quantitatively describe the tradeoffs in design of actual systems.