We continue the study of Mastrovito form of Karatsuba (MK) multipliers under the shifted polynomial basis (SPB). An MK multiplier utilizes Karatsuba algorithm and Mastrovito approach to optimize polynomial multiplication and modular reduction, which lead to a better space and time tradeoff for all trinomials. Based on this work, we make two types of contributions: 1) We derive a new modular reduction formulation for constructing Mastrovito matrix associated with special types of pentanomials, i.e., Types I, II, and Type C.1 pentanomial. Through related formulations, we demonstrate that Type I pentanomial is less efficient than Type II because of a more complicated modular reduction under the same SPB; conversely, Type C.1 pentanomial is as good as Type II under generalized polynomial basis (GPB). 2) We introduce a new MK multiplier for Type II pentanomial. It is shown that our proposal is only one TX slower than the fastest quadratic multipliers for Type II pentanomial, but its space complexity is roughly 3/4 of those schemes. To the best of our knowledge, it is the first time for hybrid multiplier to achieve such a time delay bound.
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Fast Hybrid Karatsuba Multiplier for Type II Pentanomials