Correctness problem of the threshold method of modular sharing of secrets with masking transformation

The article formulates the principles of constructing threshold cryptographic schemes for secret sharing based on a modular coding and a linear masking function with an additive variational component of pseudo-random type. The main attention is paid to the correctness problem of schemes of the considered class within the limits of the accepted model. The congruent condition in the module of the secret-original ring of the masking function values in full and partial modular number systems is obtained. On the basis of the above-said, the method of correct implementation of the threshold principle of secret information sharing is developed. The proposed approach to solving the problem under study is demonstrated by specific numerical examples.