## Cryptology ePrint Archive: Report 2006/035

Parallel Itoh-Tsujii Multiplicative Inversion Algorithm for a Special Class of Trinomials

Francisco Rodríguez-Henríquez and Guillermo Morales-Luna and Nazar A. Saqib and Nareli Cruz-Cortés

Abstract: In this contribution, we derive a novel parallel formulation of the standard Itoh-Tsujii algorithm for multiplicative inverse computation over GF($2^m$). 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($2^193$) after 20 clock cycles in about $0.94\mu$S.

Category / Keywords: foundations / number theory, implementation