Effect of Cover Quantization on Steganographic Fisher Information

The square-root law of imperfect steganography ties the embedding change rate and the cover length with statistical detectability. In this paper, we extend the law to consider the effects of cover quantization. Assuming the individual cover elements are quantized i.i.d. samples drawn from an underlying continuous-valued “precover” distribution, the steganographic Fisher information scales as Δ”, where Δ is the quantization step and is determined jointly by the smoothness of the precover distribution and the properties of the embedding function. This extension is relevant for understanding the effects of the pixel color depth and the JPEG quality factor on the length of secure payload.