Construction of optical Hash function based on nonlinear cascaded Fourier transform

A method of constructing optical Hash function based on nonlinear cascaded Fourier transform is proposed. The proposed method consists of two single one-way encryption processes. In the first process, the digital information is divided to several data blocks with 512-bit each. The data blocks are encoded to 8 by 8 sub-images with 256 gray scales, creating information planes. Then take a nonlinear cascaded Fourier transform of sub-image to generate a data matrix through an optical/digital hybrid system. By extending the data matrix we get four information planes. Again, taking nonlinear cascaded Fourier transform to built information planes, we get a Hash value 64-bit long (hash(1)). In the second process, we shift cydically every numerical value of the original information planes by 4-bit, constructing auxiliary information planes. Thereafter we take the same operations as we have done in the first process to the Hash value (hash(2)). Once hash(1) and hash(2) obtained, they are combined to form a final Hash value 128-bit long (hash). Furthermore, the avalanche effect coefficient (AEC) was also proposed to evaluate the performance of the optical Hash function. Theoretical analysis and simulation results are presented to show the effectiveness of optical Hash function constructed by our approach and the constructed optical Hash function has good performance of avalanche effect and collision resistance.