  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.
