This work presents the results of the author’s research on the protection of mathematical formulas through use of functional invariants. This paper describes in detail the methods of transforming mathematical formulas to hide their dependencies while maintaining the correctness of expressions and the invariance of results generated by the source formulas. Application of such additive and multiplicative invariants as variables, numeric values, and operators to the structural elements of a mathematical formula is also shown.

This work presents the author’s original research on engineering of algorithms to modify smart household appliance operation with a particular emphasis on ensuring the achievement of a controlled lifetime. The presented solutions are based on the programmable process of device interaction with the user, simulated damage, and simulated wear of the device. These solutions are particularly important in business processes aimed at increasing profit as a result of the quiet pressure for end users to replace household appliances more frequently.

This paper presents the results of the author’s research on the design of hidden communication algorithms employed in the context of global exchange services. The solutions proposed enable communication between trading participants without use of such traditional communication routes as email, telephone, instant messaging, discussion forums, etc. The solutions described are based on modification of entries in the exchange tables of orders and transactions. Through modification of the entries associated with share buy and sell orders, a secret channel can be constructed through which hidden messages can be sent. Such messages could, for example, be used to manipulate stock prices by an organized group of people. The proposed solutions can classified as steganographic methods where the message carrier is a stock transaction or stock order table, in which a message is embedded by means of algorithmic modification of buy and sell records. Also presented are specific proposals for static, dynamic, and mixed static-dynamic solutions based on the results of the author’s research. In the static methods group, an imperceptible communication channel is formed through a series of asynchronous modifications that create a complete, readable message that is present for a relatively long time. In dynamic methods, the embedded message is synchronized in time and creates a sequence of events that create statements. The third group of methods presented, mixed methods, use static and dynamic techniques to construct hidden messages. In particular, the method of extreme orders (MEO), mono-table method (MTM), multi-table method (MUTM), method of price-indexed vectors (MPIV), method of quantity-indexed vectors (MQIV), clustered order method (COM), distributed order method (DOM), position-encoded method (PEM), method with quantity coding (MQC), method with error correction (MEC), method limited to buy orders (MLBO), method limited to sell orders (MLSO), and self-synchronizing method (SSM) are presented. The solutions presented in this work can be applied practically in any publicly available stock trading system in which order tables are available. The algorithms presented in the paper were implemented and verified on a real trading service, and the research software used was implemented based on the API provided by the brokerage office.