New efficient bit-parallel polynomial basis multiplier for special pentanomials

Author-Highlights
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• We propose a new bit-parallel polynomial basis multiplier for finite field.
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• We induce multipliers for types I and II pentanomials using presented approach.
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• The proposed multipliers for types I and II pentanomials have the lowest complexity.

We present a bit-parallel polynomial basis multiplier based on a new divide-and-conquer approach using squaring. In particular, we apply the proposed approach to special types of irreducible pentanomials called as types I and II pentanomials, and induce explicit formulae and complexities of the proposed multiplier for these types of pentanomials. As a result, the proposed multiplier for type I pentanomials has almost the same time complexity, but about 25% reduced space complexity compared with the best known results in the literature. For type II pentanomials, we obtain the multiplier which has the lowest time complexity and about 25% reduced space complexity than the best known polynomial basis multipliers.