An Alternative Approach to Polynomial Modular Number System Internal Reduction

The Polynomial Modular Number System (PMNS) is an alternative to the binary multi-precision representation that allows transport arithmetic of a finite field polynomial ring. most important operation in system internal reduction follows any operation. All recent works on subject use same algorithm derived from Montgomery's modular multiplications perform this reduction. This paper designs and analyzes two algorithms reduction, both based Babai's Closest Vector algorithms. It significantly reduce number additions needed A comprehensive experimental analysis shows one those also faster practice. For matter, C code generation tool has been developed order produce implementations for prime field.