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Since the first appearance in Fridrich's design, the usage of permutation-diffusion structure for designing digital image cryptosystem has been receiving increasing research attention in the field of chaos-based cryptography. Recently, a novel chaotic image cipher using a single-round modified permutation-diffusion pattern (ICMPD) was proposed. Unlike traditional permutation-diffusion structure, the permutation of ICMPD is operated on bit level instead of pixel level and its diffusion stage is operated on masked pixels, which are obtained by carrying out the classical affine cipher, instead of plain pixels. Following a divide-and-conquer strategy, this paper reports that ICMPD can be compromised by a chosen-plaintext attack efficiently and the involved data complexity is linear to the size of the plain-image. Moreover, the relationship between the cryptographic kernel at the diffusion stage of ICMPD and the classical modulo addition then XORing operation is explored thoroughly.

Chosen-plaintext attack of an image encryption scheme based on modified permutation–diffusion structure