METHOD AND APPARATUS FOR PERFORMING MULTIPLICATION IN FINITE FIELD GF(2N)

A method of obtaining C=(c0, . . . , cn−1) of a product of two elements A and B of a finite field GF(2n). The method includes permuting the last d coefficients (an−1, . . . , an−d) of a multiplier A with predetermined variables (sn−1, . . . , sn−d); operating C:C=⊕(bi+j●A) for (I+j)th coefficient of a multiplicand B to update coefficients of C, where i and j are integers, and A:=(s, . . . ,αx−2)⊕(0,xn−1−j●f1, . . . ,sx−1−j●fx−d,0, . . . ,0) repeatedly for j=0 to (d−1) to update coefficients of A, where ⊕ represents an XOR operation and ● represents an AND operation; and repeatedly performing the permuting and operating by increasing i from 0 to (n−1) by d.