Multi-party secure computation of multi-variable polynomials

The goal of decentralizing the calculations performed by participants in information interaction protocols is usually to improve the reliability and security of information systems. Decentralized computing is based on multi-party secure computing protocols (MSCP), which are usually not universal, but are built for pre-specific functions calculated by participants. In this work, an MSCP is constructed to calculate polynomial values from several variables over a finite field. The constructed protocol is based on linear secret separation schemes, and its characteristics, such as the power of valid and unauthorized coalitions, can be described in terms of the characteristics of linear codes and their Schur-Hadamard degrees. Some codes and code constructs for which such characteristics can be determined analytically are described.