Patent Document ID: 6038581
Application ID: 09014891
Patent Flag: 1

Claim One:
1. A method for calculating a multiplicative inverse in finite field GF(2.sup.2n), comprising the steps of: expressing an element m.di-elect cons.GF(2.sup.2n) as EQU m=x.alpha.+y(.alpha.+1)(x,y.di-elect cons.GF(2.sup.n)) where .alpha..di-elect cons.GF(2.sup.2n).backslash.GF(2.sup.n), .alpha..sup.2 +.alpha.+a=0, and a.di-elect cons.GF(2.sup.n) so that a multiplicative inverse m.sup.-1 of the element m in the finite field GF(2.sup.2n) is expressed as a combination of multiplications, additions and a multiplicative inverse calculation in subfield GF(2.sup.n) given by EQU m.sup.-1 =(a(x+y).sup.2 +xy).sup.-1 y.alpha.+(a(x+y).sup.2 +xy).sup.-1 x(.alpha.+1) by combining a normal basis [.alpha. .alpha.+1] with extended Euclidean algorithm; and calculating the multiplicative inverse m.sup.-1 of the element m in the finite field GF(2.sup.2n) by executing said combination of multiplications, additions and a multiplicative inverse calculation in the subfield GF(2.sup.n).