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Efficient squarer for Type C.2 pentanomial

Efficient squarer for Type C.2 pentanomial

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In recent years, two new types of irreducible pentanomials, i.e. Type C.1 and Type C.2 pentanomials, and their associated generalised polynomials bases (GPBs) have been proposed to yield efficient bit-parallel multiplier architectures. The GPB squarer for Type C.1 pentanomial is also investigated previously. But no GPB squarer for Type C.2 pentanomial is given as these pentanomials are far more complicated. In this Letter, the authors give explicit GPB squarer formulae for all Type C.2 pentanomials by re-classifying these pentanomials into certain sub-groups, which is based on the parities of pentanomial parameters. As the main contribution of this Letter, the authors show that the GPB squarers for most Type C.2 pentanomials match the fastest results.

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      • 3. Wu, H.: ‘Montgomery multiplier and squarer for a class of finite fields’, Trans. Comput., 2003, 51, (5), pp. 521529.
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