Optimal quantitative cryptanalysis of permutation-only multimedia ciphers against plaintext attacks

Recently, an image scrambling encryption algorithm of pixel bit based on chaos map was proposed. Considering the algorithm as a typical binary image scrambling/permutation algorithm exerting on plaintext of size M×(8N), this paper proposes a novel optimal method to break it with some known/chosen-plaintexts. The spatial complexity and computational complexity of the attack are only O(32·MN) and O(16·n0·MN) respectively, where n0 is the number of known/chosen-plaintexts used. The method can be easily extended to break any permutation-only encryption scheme exerting on plaintext of size M×N and with L different levels of values. The corresponding spatial complexity and computational complexity are only O(MN) and O(logL(MN)⌉·MN) respectively. In addition, some specific remarks on the performance of the image scrambling encryption algorithm are presented.