**Bit-Parallel $GF(2^{n})$ Squarer Using Shifted Polynomial Basis**

*Xi Xiong and Haining Fan*

**Abstract: **We present explicit formulae and complexities of bit-parallel shifted polynomial basis (SPB)
squarers in finite field $GF(2^{n})$s generated by general irreducible trinomials
$x^{n}+x^{k}+1$ ($0< k <n$) and type-II irreducible pentanomials
$x^{n}+x^{k+1}+x^{k}+x^{k-1}+1$ ($3<k<(n-3)/2$). The complexities of the proposed squarers
match or slightly outperform the previous best results.
These formulae can also be used to design polynomial basis Montgomery squarers without any change.
Furthermore, we show by examples that
XOR gate numbers of SPB squarers are different when different shift factors in
the SPB definition, i.e., parameter $v$ in ${\{}x^{i-v}|0\leq i\leq n-1 {\}}$, are used.
This corrects previous misinterpretation.

**Category / Keywords: **

**Date: **received 4 Nov 2012

**Contact author: **xiongxi08 at gmail com; fhn@tsinghua edu cn

**Available format(s): **PDF | BibTeX Citation

**Version: **20121108:153602 (All versions of this report)

**Short URL: **ia.cr/2012/626

**Discussion forum: **Show discussion | Start new discussion

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