Patent ID: 7167886

Claim:
A device for calculating an inversion in finite field GF(2 2n ), wherein n is a positive integer, comprising: (a) means for expressing an element eεGF(2 2n ) as e=x 0 α+x 1 α 2 ( x 0 ,x 1 εGF (2 n )) where α+α 2 =1 so that an inverse e −1 of said element e in said finite field GF(2 2n ) is expressed as a combination of arithmetic operations performed in subfield GF(2 n ) given by e −1 =( x 1 /N )α+( x 0 /N )α 2 where N=(x 0 2 +x 1 2 )+x 0 x 1 εGF(2 n ) by using an optimal normal basis of order 2 {α, α 2 }; and (b) means for calculating said inverse e −1 of said element e in said finite field GF(2 2n ) by executing said combination of arithmetic operations in said subfield GF(2 n ).