Mathematical model of a steganographic system based on key information in the form of stegosets

A formal description of the mathematical model of a steganographic system based on key information in the form of stegosets is given. The mathematical model of the steganographic system is intended both for placing hidden marks to control the integrity of documents acting as a container, and for covert data transmission. Exist-ing mathematical models do not fully meet the requirements for steganographic systems. The proposed model is based on the concepts of a three-level key, a stegoset, a container component, and a message block. The three-level key is a set of actual steganographic transformations depending on the type of container. A stegoset is an element of a key set. A component of a container is such a subset of it that there is a stegoset for it. A message block is such a sequential part of the message that there is a container component for it, in which it can be hidden using the appropriate stegoset. The model implements the application of different stegosets to different container compo-nents, and the message can be divided into blocks. The model allows controlling the integrity of the message and adapts to different types of containers. Possible options for the practical application of the mathematical model are proposed, such as monitoring the integrity of the message when calculating the control number, splitting the message into blocks and sequentially monitoring their integrity by analogy with the blockchain system.