Secret Sharing Scheme with Share Verification Capability

This paper examines the properties of classical secret sharing schemes used in information protection systems, including the protection of valuable and confidential data. It addresses issues such as implementation complexity, limited flexibility, vulnerability to new types of attacks, the requirements for such schemes, and analyzes existing approaches to their solutions. A new secret sharing scheme is proposed as a potential solution to these challenges. The developed scheme is based on multivariable functions. The shares distributed among participants represent the values of these functions. Secret reconstruction is reduced to solving a system of linear equations composed of such functions. The structure and mathematical foundation of the scheme are presented, along with an analysis of its properties. A key feature of the proposed scheme is the incorporation of functions aimed at authenticating participants and verifying the integrity of the distributed shares. The paper also provides a cryptanalysis of the scheme, evaluates its resistance to various types of attacks, and discusses the results obtained. Thus, this work contributes to the advancement of information security methods by offering a modern and reliable solution for the secure storage and joint use of secret data.