Circuit for calculating the inverse of an arbitrary element of a finite field

摘要

A combinational logic type inversion circuit for calculating the inverse of an arbitrary element &agr;.sup.i in a finite field, includes a power and multiplication circuit for calculating a primitive element . alpha..sup.i raised to the (2.sup.1)-th power through a primitive element &agr;.sup.i raised to the (2.sup.m-1)-th power and multiplying all of the primitive elements &agr;.sup.i raised to the (2. sup.1)-th power through &agr;.sup.i raised to the (2.sup.m-1)-th power together to generate an output M.sub.OUT, and a divider circuit for dividing the output M.sub.OUT of the power and multiplication circuit by the primitive element &agr; raised to the (2.sup.m -1)-th power.