Speeding up Subquadratic Finite Field Multiplier over GF(2m) Generated by Trinomials Using Toeplitz Matrix-Vector with Inner Product Formula

A new four way split method of bit-level Toeplitz matrix-vector product for computing trinomial-based multiplier over GF(2^m) is presented. The proposed scheme is based on two way splitting method to use Toeplitz matrix-vector product using inner product (TMVPIP) formula. Applying the proposed TMVPIP architecture, it is shown that the computation time of proposed sub quadratic multiplier can be reduced from O(log₂m) of the existing sub quadratic multipliers to O(log₂log₂m). Our proposed sub quadratic multiplier with TMVPIP formula is suitable for efficient implementation of the point multiplication in Koblitz curves.