Computational and implementation complexity of polynomial evaluation schemes

Abstract

In this work, we consider the computational complexity of different polynomial evaluation schemes. By considering the number of operations of different types, critical path, pipelining complexity, and latency after pipelining, high-level comparisons are obtained. These can then be used to short list suitable candidates for an implementation given the specifications. Not only multiplications are considered, but they are divided into data-data multiplications, squarers, and data-coefficient multiplications, as the latter can be optimized depending on implementation architecture and application.