Optical multilevel authentication based on singular value decomposition ghost imaging and secret sharing cryptography

Abstract An optical multilevel authentication method is proposed that is based on the singular value decomposition ghost imaging (SVDGI) and (t, n) threshold secret sharing scheme. SVDGI provides an efficient reconstruction method in ghost imaging (GI) by modifying the measurement matrix with the help of singular value decomposition, which enables the reconstruction of an N-pixel image utilizing much less than N measurements with less time and a higher quality. On the other hand, the (t, n) threshold secret sharing algorithm guarantees the multilevel authentication system, in which, the modified measurement matrix is grouped into n parts as n keys and distributed to n different participants, any t (t ≤ n) or more of authorized participants with their correct keys can be collected to restore the original meaningful certification image, which is so called the high-level authentication; While in the case of low-level authentication, any t - 1 or fewer will gain no exact information of the certification image, but a remarkable peak output can be acquired in the 3D distribution of the nonlinear correlation coefficient of the standard certification image and the recovered image. So that the method successfully provides a multilevel authentication. Both numerical simulations and optical experiments validate the feasibility of the proposed method.