  Authentication mechanisms are at the forefront of defending the world from
various types of cybercrime. Steganography can serve as an authentication
solution through the use of a digital signature embedded in a carrier object to
ensure the integrity of the object and simultaneously lighten the burden of
metadata management. Nevertheless, despite being generally imperceptible to
human sensory systems, any degree of steganographic distortion might be
inadmissible in fidelity-sensitive situations such as forensic science, legal
proceedings, medical diagnosis and military reconnaissance. This has led to the
development of reversible steganography. A fundamental element of reversible
steganography is predictive analytics, for which powerful neural network models
have been effectively deployed. Another core element is reversible
steganographic coding. Contemporary coding is based primarily on heuristics,
which offers a shortcut towards sufficient, but not necessarily optimal,
capacity--distortion performance. While attempts have been made to realise
automatic coding with neural networks, perfect reversibility is unattainable
via such learning machinery. Instead of relying on heuristics and machine
learning, we aim to derive optimal coding by means of mathematical
optimisation. In this study, we formulate reversible steganographic coding as a
nonlinear discrete optimisation problem with a logarithmic capacity constraint
and a quadratic distortion objective. Linearisation techniques are developed to
enable iterative mixed-integer linear programming. Experimental results
validate the near-optimality of the proposed optimisation algorithm when
benchmarked against a brute-force method.
