Deciphering an Image Cipher Based on Mixed Transformed Logistic Maps

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 87 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.