Finite field inversion over the dual basis

摘要

In this transaction brief we consider the design of dual basisninversion circuits for GF(2m). Two architectures arenpresented-one bit-serial and one bit-parallel-both of which are based onnFermat's theorem. Finite field inverters based on Fermat's theorem havenpreviously been presented which operate over the normal basis and thenpolynomial basis. However there are two advantages to be gained bynforcing inversion circuits to operate over the dual basis. First, theseninversion circuits can be utilized in circuits using hardware efficientndual basis multipliers without any extra basis converters. And second,nthe inversion circuits themselves can take advantage of dual basisnmultipliers, thus reducing their own hardware levels. As both thesenapproaches require squaring in a finite field to take place, a theoremnis presented which allows circuits to be easily designed to carry outnsquaring over the dual basis