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

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 costly 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.

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