  Conventional covert image communication is assumed to transmit the message,
in the securest way possible for a given payload, over lossless channels, and
the associated steganographic schemes are generally vulnerable to active
attacks, e.g., JPEG re-compression, scaling, as seen on social networks.
Although considerable progress has been made on robust steganography against
JPEG re-compression, there exist few steganographic schemes capable of
resisting to scaling attacks due to the tricky inverse interpolations involved
in algorithm design. To tackle this issue, a framework for robust image
steganography resisting to scaling with general interpolations either in
standard form with fixed interpolation block, or pre-filtering based
anti-aliasing implementation with variable block, is proposed in this paper.
And the task of robust steganography can be formulated as one of constrained
integer programming aiming at perfectly recover the secret message from stego
image while minimizing the difference between cover and stego images. By
introducing a metric - the degree of pixel involvement (dPI) to identify the
modifiable pixels in cover image, the optimization problem above could be
effectively solved using branch and bound algorithm (B\&B). In addition, a
customized distortion function for scaled stego images is adopted to further
boost the security performance. Extensive experiments are carried out which
demonstrate that the proposed scheme could not only outperform the prior art in
terms of security by a clear margin, but also be applicable to resisting the
scaling attacks with various interpolation techniques at arbitrary scaling
factors (SFs).
