PARALLEL MULTIPLICATION METHOD AND APPARATUS USING DICKSON BASIS ON FINITE FIELD GF(2^N)

摘要

The present invention relates to a parallel multiplication method using a Dickson basis on a finite field GF(2ⁿ), comprising: a step in which a matrix generation unit receives element a of the finite field GF(2ⁿ) as a vector (a_i, a₂,... a_n) so as to form symmetric Toeplitz matrix S and upper triangular Toeplitz matrix U; a step in which a vector output unit receives element b of the finite field GF(2ⁿ) as a vector (b_i, b₂,... b_n) so as to calculate products (SB, UB and UB') of the Toeplitz matrices S and U and output the products as vectors; a step in which a vector sum output unit calculates and outputs a sum (SB+UB') of the two calculated vectors (SB and UB'); and a step in which a vector conversion unit receives the vectors (SB+UB' and UB) so as to convert the vectors (SB+UB' and UB) to a coordinate vector (c_i, c₂,... c_n) of c, which is a product of the two elements a and b.