On the effective subkey space of some image encryption algorithms using external key

•Show the importance of properly designing the key schedule of image encryption.•A new rule to ensure that subkeys retain the key space security of image encryption.•Attacks on three schemes to show how the rule is applied to concrete schemes.

One of the general ways in designing a secure image encryption algorithm based on chaos theory is to derive a number of round subkeys from the Key Schedule algorithm under the control of an external secret key. A compulsory condition for the security of an image encryption algorithm is that the length of the external secret key should be sufficiently long in terms of bitlength. However, the sufficiently long secret key is not a guarantee that the algorithm is secure. In this paper, we emphasize the importance in designing a secure Key Schedule algorithm for such image based encryption techniques. Notably, we show why the effective space spanned by the subkeys should never be smaller than the external secret key space. To highlight the importance of this, we present our attacks on three recently proposed image encryption schemes.