  During the past decades, there is a great popularity employing nonlinear
dynamics and permutation-substitution architecture for image encryption. There
are three primary procedures in such encryption schemes, the key schedule
module for producing encryption factors, permutation for image scrambling and
substitution for pixel modification. Under the assumption of chosen-ciphertext
attack, we evaluate the security of a class of image ciphers which adopts
pixel-level permutation and modular addition for substitution. It is
mathematically revealed that the mapping from differentials of ciphertexts to
those of plaintexts are linear and has nothing to do with the key schedules,
permutation techniques and encryption rounds. Moreover, a universal
chosen-ciphertext attack is proposed and validated. Experimental results
demonstrate that the plaintexts can be directly reconstructed without any
security key or encryption elements. Related cryptographic discussions are also
given.

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