  Laser speckle has been proposed in a number of papers as a high-entropy
source of unpredictable bits for use in security applications. Bit strings
derived from speckle can be used for a variety of security purposes such as
identification, authentication, anti-counterfeiting, secure key storage, random
number generation and tamper protection. The choice of laser speckle as a
source of random keys is quite natural, given the chaotic properties of
speckle. However, this same chaotic behaviour also causes reproducibility
problems. Cryptographic protocols require either zero noise or very low noise
in their inputs; hence the issue of error rates is critical to applications of
laser speckle in cryptography. Most of the literature uses an error reduction
method based on Gabor filtering. Though the method is successful, it has not
been thoroughly analysed.
  In this paper we present a statistical analysis of Gabor-filtered speckle
patterns. We introduce a model in which perturbations are described as random
phase changes in the source plane. Using this model we compute the second and
fourth order statistics of Gabor coefficients. We determine the mutual
information between perturbed and unperturbed Gabor coefficients and the bit
error rate in the derived bit string. The mutual information provides an
absolute upper bound on the number of secure bits that can be reproducibly
extracted from noisy measurements.

Cryptography and Security;Computer Vision and Pattern Recognition