1. A method for authenticating an object, comprising: providing a set of elements, physically associated with the object, having an original physical random dispersion pattern, each element having a specific predetermined optical characteristic which is not representable as a CIE tristimulus value due to at least one of dichrosim, fluorescence, phosphorescence, refraction, diffraction, lasing, and hyperspectral color characteristics; determining the original physical random dispersion pattern of the set of elements; generating a cryptographically authenticated secure digital signature code from a cryptographic one-way trap door function, from which the original physical dispersion pattern cannot be ascertained, but the identity of a measured physical dispersion pattern and the original physical random dispersion represented in the digital signature code can be verified, being pre-encoded to provide a tolerance to a predefined variation between the original physical random dispersion pattern and the measured physical dispersion pattern; associating the digital signature code with the object; and authenticating the object by: optically illuminating the set of elements; reading the digital signature code; optically reading the positions and characteristics of the set of elements associated with the object to obtain the measured physical dispersion pattern; verifying that the set of optically read elements have the specific predetermined optical characteristic; and verifying a correspondence of measured physical dispersion pattern and the original physical random dispersion pattern represented by the digital signature code, wherein a counterfeiting of the physical random dispersion pattern is impeded by a requirement for an accurate placement of the set of physical elements to correspond to the digital signature code and a requirement for the set of elements to accurately display the specific predetermined optical characteristic which is not representable as a CIE tristimulus value due to at least one of dichrosim, fluorescence, phosphorescence, refraction, diffraction, optical conduction, lasing, and hyperspectral color characteristics.