Unlike most research involving finite field multipliers, this work targets a low-power multiplier through the application of various power reduction techniques to different types of multipliers and comparing their power consumption among other factors, rather than comparing complexity measures such as gate count or area. Gate count is used as a starting point to choose potential architectures, namely, polynomial and normal basis architectures. Power reduction techniques employed are mainly concerned with Architecture- and Logic-Level low-power techniques. They include supply voltage reduction, power cost estimations, using low-power logic families and pipelining.