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In this paper, three small classes of finite fields GF(2m) are found for which low complexity bit-parallel multipliers are proposed. The proposed multipliers have lower complexities compared to those based on the irreducible pentanomials. It is also shown that there does not always exist an irreducible all-one polynomial, equally-spaced polynomial, or trinomial for the new classes of fields.
This short paper summarizes our recent results on construction of low-complexity bit-parallel finite field multiplier using polynomial basis. The complexity and time delay of the proposed multipliers are lower than those of the similar proposals.
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