Construction of Perfect Form of Residue Number System for Gaussian Integers to Asymmetric Cryptosystems

This article presents the theoretical foundations and a method for finding a system of modules of the perfect form of the residue number system in the complex domain based on fractional transformations. The proposed approach allows to reduce the computational complexity of cryptographic algorithms by avoiding the most labour-intensive operation - finding the modular inverse. As a result of the studies conducted, it has been shown that the proposed method significantly reduces the computational complexity of the Chinese Remainder Theorem. Examples of the computation of the possible values of the sought modules using the developed method are given.