Analysis of algorithms performing basic arithmetic operations in the quadratic RNS

Abstract

In this paper we explore the question of representing complex numbers in a residue number system and build algorithms for the operations of addition and multiplication. The idea of the construction of such systems is in determining how the set of complex numbers the ring of integers. The main attention is paid to quadratic residue number system. The idea of building such a system is to provide a complex number z as a pair of integers (X' Y for the selected modules. The rules of arithmetic operations on complex numbers presented residue pairs at selected bases, do not differ from the rules of arithmetic operations in the RNS for real integers. The operations of addition and multiplication two complex numbers in quadratic RNS is modular, parallel channels and contains only two arithmetic operations that can reduce the volume of calculation.