Parallel Itoh-Tsujii multiplicative inversion algorithm for a special class of trinomials

In this contribution, we derive a novel parallel formulation of the standard Itoh-Tsujii algorithm for multiplicative inverse computation over 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) = Xm + Xk + 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?S.

• Type: Conference
• Year: 2007
• Where: DCC
• Authors: Francisco Rodríguez-Henríquez, Guillermo Morales-Luna, Nazar A. Saqib, Nareli Cruz Cortés
• Keywords: Computer Graphics, DCC 2007, Field Square Root, Multiplicative Inverse Computation, Standard Itoh-tsujii Algorithm