Fast Bit Parallel-Shifted Polynomial Basis Multipliers in GF(2n)

A new nonpipelined bit-parallel-shifted polynomial basis multiplier for GF(2ⁿ) is presented. For some irreducible trinomials, the space complexity of the multiplier matches the best results available in the literature, and its gate delay is equal to T _A+lceillog₂nrceilT_X, where T_A and T_X are the delay of one two-input and and xor gates, respectively. To the best of our knowledge, this is the first time that the gate delay bound T_A+lceillog₂nrceilT_X is reached. For some irreducible pentanomials, its gate delay is equal to T_A +(1+lceillog₂nrceil)T_X. NIST has recommended five binary fields for the elliptic curve digital signature algorithm applications: GF(2¹⁶³), GF(2²³³), GF(2 ²⁸³), GF(2⁴⁰⁹), and GF(2⁵⁷¹), but no irreducible trinomials exist for three degrees, viz., 163, 283 and 571. For the three corresponding binary fields, we show that the gate delay of the proposed multiplier is T_A+(1+lceillog₂nrceil)T_X. This result outperforms the previously known results