Statistical test criteria for sensitivity indexes of image cryptosystems

Abstract

System sensitivity is an important security evaluation aspect of image cryptosystems. On the basis of probability and statistics this paper studies in detail the theoretical-value calculation methods of sensitivity evaluation indexes of image cryptosystems: the expected values and variances of NPCR (number of pixels change rate), UACI (unified average changing intensity), and BACI (blocked average changing intensity). Also, the acceptance domains of listed indexes are discussed using the central limit theorem, and five image cryptosystems are employed to test the acceptance domains. Finally, the following conclusion is drawn: the image cryptosystem is identified as sensitive when the passing rate of the BACI index of multiple tests is higher than 50% under the conditions that the number of samples is 100 and the significance level is α = 0.01, or when the maximum relative error of the average values of the BACI indexes of multiple tests is less than 0.1%.