# A Model and Quantitative Framework for Evaluating Iterative Steganography
## 1 Introduction
### Steganography  
A wide range of steganographic techniques has been extensively documented in the literature [4]. The primary goal of these methods is to encode information within a digital cover medium, producing a steganogram that closely resembles the original cover. This resemblance is intended to make the detection of embedded messages highly challenging or practically infeasible [5]. The choice of a suitable steganographic technique depends on several factors [6], including the type of the cover medium, which may consist of text files, digital images, audio streams, video sequences, or network transmissions. Moreover, the selection is influenced by specific requirements regarding the desired properties of the steganographic method, such as capacity, robustness, and undetectability [7]. In recent years, one of the most actively investigated directions in research on steganographic techniques has been the domain of machine learning, including the use of neural networks. One of the latest examples of a novel approach advancing steganographic techniques can be found in the paper [8], which introduces an innovative invisible androbust watermarking model for digital images. It employs hierarchical residual fusion and multi-scale convolution techniques to embed imperceptible yet resilient watermarks. The proposed neural network-based approach aims to balance image quality preservation with watermark durability against various image manipulations, likely demonstrating improved PSNR, SSIM, and resistance to common image transformations. Another example can be found in [9]. This paper introduces a novel dual color image watermarking scheme utilizing quaternion fractional-order orthogonal Fourier-Mellin moments and least square support vector regression for geometric correction. The method employs advanced techniques including 3D sine map encryption, lifting wavelet transform, and quaternion discrete Fourier transform to enhance security and robustness. Experimental results demonstrate high imperceptibility and strong robustness against various attacks, representing a significant advancement in color image watermarking and copyright protection. Although the various approaches found in the literature are highly valuable in multiple respects and advance the field of steganography in several promising directions, the literature lacks any references directly addressing the core topic of our work, i.e., the formalization and quantification of the fundamental properties of iterative steganography. We utilize three fundamental metrics to define the core properties of steganographic techniques. These metrics are often interdependent and involve trade-offs in steganographic system design. Achieving the optimal balance between these properties depends on the specific application requirements and the anticipated threats to the steganographic communication channel:  
* Undetectability: this metric evaluates a steganographic technique's ability to conceal information within a steganogram so that its presence remains imperceptible to both human perception and statistical detection methods [10]. High undetectability signifies that the alterations introduced into the cover medium are minimally noticeable and resistant to detection [11],
* Capacity: this metric measures the amount of information that can be embedded within a digital cover medium without causing noticeable degradation in its quality. Capacity depends on the characteristics of the cover medium and the chosen steganographic technique. While higher capacity enables greater information concealment, it may reduce undetectability by increasing the likelihood of detection [12],
* Robustness: this metric assesses a steganographic technique's resilience in preserving embedded information when subjected to various disruptions or transformations, such as compression, format conversion, filtering, rotation, or scaling.