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Available under a Creative Commons Attribution Non-Commercial Share Alike 4.0 International Licence


1.1 MATHMATICS, Computer Sciences


The unification of data encryption with information hiding methods continues to receive significant attention because of the importance of protecting encrypted information by making it covert. This is because one of the principal limitations in any cryptographic system is that encrypted data flags the potential importance of the data (i.e. the plaintext information that has been encrypted) possibly leading to the launch of an attack which may or may not be successful. Information hiding overcomes this limitation by making the data (which may be the plaintext or the encrypted plaintext) imperceptible, the security of the hidden information being compromised if and only if its existence is detected.

We consider two functions f1(r) and f2(r) for r ∈ R n , n = 1, 2, 3, ... and the problem of ‘Diffusing’ these functions together, applying a process we call ‘Stochastic Diffusion’ to the diffused field and then hiding the output of this process into one of the two functions. The coupling of these two processes using a form of conditioning that generates a well-posed inverse solution yields a super-encrypted field that is dataconsistent.

After presenting the basic encryption method and (encrypted) information hiding model coupled with a mathematical analysis (within the context of ‘convolutional encoding’), we provide a case study which is concerned with the implementation of the approach for full-colour 24-bit digital images. The ideas considered yields the foundations for a number of wide-ranging applications that include covert signal and image information interchange, data authentication, copyright protection and digital rights management. In this context, we also provide prototype software using m-code and Python for readers to use, improve upon and develop further for applications of interest.