The paper considers the application of polynomial residue number system for construction of fully homomorphic encryption codes. As an example of computational system the realization of the secret sharing scheme is considered, where polynomials of the form \(p_i(x)=x^{15}+x^a+1\) are taken as moduli of the system. The obtained system of homomorphic encryption based on polynomial residue number system can be used both in the construction of cryptographic coprocessors and implemented as algorithms for distributed and cloud computing.