  This paper re-evaluates the security of a chaotic image encryption algorithm
called MCKBA/HCKBA and finds that it can be broken efficiently with two known
plain-images and the corresponding cipher-images. In addition, it is reported
that a previously proposed breaking on MCKBA/HCKBA can be further improved by
reducing the number of chosen plain-images from four to two. The two attacks
are both based on the properties of solving a composite function involving the
carry bit, which is composed of the modulo addition and the bitwise OR
operations. Both rigorous theoretical analysis and detailed experimental
results are provided.
