Note on Modular Reduction in Extended Finite Fields and Polynomial Rings for Simple Hardware

Abstract

Modular reduction in extended finite fields and polynomial rings is presented, which once implemented works for any random reduction polynomial without changes of the hardware. It is possible to reduce polynomials of whatever degree. Based on the principal defined, two example RTL architectures are designed, and some useful features are noted furthermore. The first architecture is sequential and reduce whatever degree polynomials, taking 2 cycles per term. The second one is Parallel and designed for reduction of polynomials of 2(t−1) degree at most, taking 1 cycle for the whole reduction.