An authentication system comprising a medium having a plurality of elements, the elements being distinctive, detectable and disposed in an irregular pattern or having an intrinsic irregularity. Each element is characterized by a determinable attribute distinct from a two-dimensional coordinate representation of simple optical absorption or simple optical reflection intensity. An attribute and position of the plurality of elements, with respect to a positional reference is detected. A processor generates an encrypted message including at least a portion of the attribute and position of the plurality of elements. The encrypted message is recorded in physical association with the medium. The elements are preferably dichroic fibers, and the attribute is preferably a polarization or dichroic axis, which may vary over the length of a fiber. An authentication of the medium based on the encrypted message may be authenticated with a statistical tolerance, based on a vector mapping of the elements of the medium, without requiring a complete image of the medium and elements to be recorded.