NPCR and UACI Randomness Tests for Image Encryption

Abstract—The number of changing pixel rate (NPCR) and the unified averaged changed intensity (UACI) are two most common quantities used to evaluate the strength of image encryption algorithms/ciphers with respect to differential attacks. Conventionally, a high NPCR/UACI score is usually interpreted as a high resistance to differential attacks. However, it is not clear how high NPCR/UACI is such that the image cipher indeed has a high security level. In this paper, we approach this problem by establishing a mathematical model for ideally encrypted images and then derive expectations and variances of NPCR and UACI under this model. Further, these theoretical values are used to form statistical hypothesis NPCR…