Deciphering a novel image cipher based on mixed transformed Logistic maps
This work exposes critical vulnerabilities in a specific image encryption scheme, which is incremental as it builds on prior cryptanalysis but significantly reduces the attack requirements.
The paper re-evaluates the security of an image cipher based on transformed logistic maps and proves it can be deciphered efficiently under two conditions: with two pairs of known plain-images at complexity O(2^18 + L) or two pairs of chosen plain-images at complexity O(L), compared to the previous method requiring 87 pairs at O(2^7 + L).
Since John von Neumann suggested utilizing Logistic map as a random number generator in 1947, a great number of encryption schemes based on Logistic map and/or its variants have been proposed. This paper re-evaluates the security of an image cipher based on transformed logistic maps and proves that the image cipher can be deciphered efficiently under two different conditions: 1) two pairs of known plain-images and the corresponding cipher-images with computational complexity of $O(2^{18}+L)$; 2) two pairs of chosen plain-images and the corresponding cipher-images with computational complexity of $O(L)$, where $L$ is the number of pixels in the plain-image. In contrast, the required condition in the previous deciphering method is eighty-seven pairs of chosen plain-images and the corresponding cipher-images with computational complexity of $O(2^{7}+L)$. In addition, three other security flaws existing in most Logistic-map-based ciphers are also reported.