Cryptanalyzing an Image Encryption Algorithm Underpinned by 2-D Lag-Complex Logistic Map

This article conducts a security analysis of an image encryption algorithm that employs 2-D lag-complex logistic map (LCLM) as a pseudorandom number generator (PRNG). This algorithm uses the sum of all pixel values in the plain image as the initial value for the PRNG, thereby influencing the randomization of basic encryption operations. However, it is observed that certain factors lead to the generation of identical pseudorandom sequences for different plain images. Capitalizing on this vulnerability, we propose a chosen-plaintext attack strategy that effectively cracks the six encryption steps through a divide-and-conquer approach. By exploiting weaknesses inherent in the 2-D LCLM, the number of required chosen plain images is significantly reduced to $ 5\cdot \log_{2}(MN)+95$5·log2(MN)+95, where $ MN$MN represents the total pixel count of the plain image.