Circuits and Methods for Performing Exponentiation and Inversion of Finite Field Elements

摘要

An exponentiation circuit for computing an exponential power of a finite field element includes combinatory logic circuits that map input digits of a multi-digit field element P to output digits of an output multi-digit field element β^2m. The exponentiation circuit is capable of computing a power of a field element without performing any multiplication operations and requires only exclusive-OR logic operations to generate the output exponential field element. A circuit for generating a multiplicative inverse of a finite field element can be constructed from a set of parallel exponentiation circuits, with each of the parallel exponentiation circuits generating a different multi-digit field element β^2m directly from the input field element β. Multiplier circuits multiply together the outputs of the parallel exponentiation circuits to generate the multiplicative inverse of the field element β.