Patent ID: 6202076
Filing Date: 2001-03-13
Classification: G06F

Abstract:
A method for calculating a rational expression in finite field GF(2.sup.2) in a form of: ##EQU17##where p, q.epsilon.GF(2.sup.2n)[X.sub.1, X.sub.2, . . . , X.sub.r ], comprising the steps of:calculating a multiplication in GF(2.sup.2n) that arises in calculations using polynomials p, q.epsilon.GF(2.sup.2n)[X.sub.1, X.sub.2, . . . , X.sub.r ] according to a multiplication formula:##EQU18##where x.sub.1, x.sub.2, y.sub.1, y.sub.2, a.epsilon.GF(2.sup.n), .alpha..epsilon slash.GF(2.sup.n), .alpha..sup.2 +.alpha.+a=0 and GF(2.sup.2n)=GF(2.sup.n)(.alpha.));calculating an inverse q.sup.-1 of q in GF(2.sup.2n) according to an inverse calculation formula:(x.alpha.+y(.alpha.+1)).sup.-1 =(a(x+y).sup.2 +xy).sup.-1 (y.alpha.+x(.alpha.+1))where x, y, a.epsilon.GF(2.sup.n), .alpha..epsilon slash.GF(2.sup.n), .alpha..sup.2 +.alpha.+a=0 and GF(2.sup.2n)=GF(2.sup.n)(.alpha.)); andcalculating p.times.q.sup.-1 by using said multiplication formula.