The Serial-out bit-level multiplication scheme is characterized by an important latency feature. It has an ability to sequentially generate an output bit of the multiplication result in each clock cycle. However, the computational complexity of the existing serial-out bit-level multipliers in    $GF$      (  $2^m$      ) using normal basis representation, limits its usefulness in many applications; hence, an optimized serial-out bit-level multiplier using polynomial basis representation is needed. In this paper, we propose new serial-out bit-level Mastrovito multiplier schemes. We show that in terms of the time complexities, the proposed multiplier schemes outperform the existing serial-out bit-level schemes available in the literature. In addition, using the proposed multiplier schemes, we present new hybrid-double multiplication architectures. To the best of our knowledge, this is the first time such a hybrid multiplier structure using the polynomial basis is proposed. Prototypes of the presented serial-out bit-level schemes and the proposed hybrid-double multiplication architectures (10 schemes in total) are implemented over both   $GF(2^{163})$       and    $GF(2^{233})$      , and experimental results are presented.
['Ebrahim A. Hasan Abdulrahman', 'Arash Reyhani-Masoleh']
High-Speed Hybrid-Double Multiplication Architectures Using New Serial-Out Bit-Level Mastrovito Multipliers