Method and apparatus for performing multiplication in finite field GF(2n)

摘要

A method of obtaining C=(c₀, . . . , c_n-1) of a product of two elements A and B of a finite field GF(2ⁿ). The method includes permuting the last d coefficients (a_n-1, . . . , a_n-d) of a multiplier A with predetermined variables (s_n-1, . . . , s_n-d); operating C:C=⊕(b_i+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_n-1-j,α₀, . . . ,α_n-2)⊕(0,s_n-1-j●f₁, . . . ,s_n-1-j●f_n-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.