Small FPGA Based Multiplication-Inversion Unit for Normal Basis Representation in GF(2m)

Jeremy Metairie, Arnaud Tisserand, Emmanuel Casseau
<span title="">2015</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/k4pq3zhykrd3hdhey2qhybwinu" style="color: black;">2015 IEEE Computer Society Annual Symposium on VLSI</a> </i> &nbsp;
Halving methods have been proposed for parallel implementation of ECC primitives on multicore processors. In hardware, they can also provide protection against some side channel attacks (thanks to parallel independent operations). But they require affine coordinates for curve points and costly inversions. We propose a new combined multiplication-inversion unit for binary field extensions and halving based ECC methods optimized for FPGAs. We target small area solutions compared to very fast but
more &raquo; ... ostly ones from state-of-art. Our solution is based on permuted normal basis, Massey-Omura multiplication and Itoh-Tsujii inversion algorithms. Our FPGA implementations show better efficiency for large fields.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/isvlsi.2015.32">doi:10.1109/isvlsi.2015.32</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/isvlsi/MetairieTC15.html">dblp:conf/isvlsi/MetairieTC15</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/smm2hzee75gwboz3lh7w6jhdem">fatcat:smm2hzee75gwboz3lh7w6jhdem</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170922092729/https://hal.inria.fr/hal-01175712/document" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/33/2d/332de60f40c12c79afbb6e0ee9261cd63a2a6f33.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/isvlsi.2015.32"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>