Generalized scheme of hidden compact storage of data of various users in a common open database

A database is an organized collection of structured information, typically stored electronically in a computer system and usually controlled by a database management system (DBMS). Confidentiality, integrity and availability are the main requirements for database security. Data within the most common types of modern databases in operation is typically stored in rows and columns in a series of tables, but other configurations are also used. The use of public networks and the development of information technologies (including cloud ones) impose new increased requirements on the formation of databases. The paramount requirement is the security of databases from unauthorized actions of both the users themselves and third-party observers (potential violators). Cryptographic security tools are becoming an important tool to meet this requirement.
In this paper, based on new (introduced by the author in a recent publication) concepts of generalized discrete differentiation and integration, a fundamentally new scheme for hidden compact storage of user group data in a common open database is proposed. The components of the table are elements of the ring $K$ that encode the data. The paper proposes to use residue rings. The database does not have subsections related to the data of individual users. The corresponding table is a component-by-component sum of individual tables built by a certain algorithm according to the data of each user. Any user can retrieve his data from the database using his own individual key. The construction of the table and the algorithms for extracting individual user data from it are carried out efficiently. A user gets the key at the time of his registration in the system, when his table (obtained on the basis of his data) is created and added to the database. The key has the form of two polynomials with coefficients from $K$ with invertible leading coefficients. At the same time, a particular user does not have the opportunity to obtain the data of other users. An outside observer (potential intruder) cannot obtain any data. The scheme allows changing and deleting data without replacing keys. Free access to the database and reuse of keys are the main advantages of the scheme.