Abstract
In this contribution, we derive a novel parallel formulation of the standard Itoh–Tsujii algorithm for multiplicative inverse computation over the field GF(2m). The main building blocks used by our algorithm are: field multiplication, field squaring and field square root operators. It achieves its best performance when using a special class of irreducible trinomials, namely, P(x) = x m + x k + 1, with m and k odd numbers and when implemented in hardware platforms. Under these conditions, our experimental results show that our parallel version of the Itoh–Tsujii algorithm yields a speedup of about 30% when compared with the standard version of it. Implemented in a Virtex 3200E FPGA device, our design is able to compute multiplicative inversion over GF(2193) after 20 clock cycles in about 0.94 μS.
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Rodríguez-Henríquez, F., Morales-Luna, G., Saqib, N.A. et al. Parallel Itoh–Tsujii multiplicative inversion algorithm for a special class of trinomials. Des. Codes Cryptogr. 45, 19–37 (2007). https://doi.org/10.1007/s10623-007-9073-6
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DOI: https://doi.org/10.1007/s10623-007-9073-6