The number of changing pixel rate (NPCR) and the

unified averaged changed intensity (UACI) are two most common

quantities used to uate 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 and UACI tests.-The　number of changing pixel rate (NPCR) and the

unified averaged changed intensity (UACI) are two most common

quantities　used　to　 uate　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 and UACI tests.