Paper 2006/035

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

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


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.

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Publication info
Published elsewhere. Unknown where it was published
number theoryimplementation
Contact author(s)
francisco @ cs cinvestav mx
gmorales @ cs cinvestav mx
2006-02-06: received
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      author = {Francisco Rodríguez-Henríquez and Guillermo Morales-Luna and Nazar A.  Saqib and Nareli Cruz-Cortés},
      title = {Parallel Itoh-Tsujii Multiplicative Inversion Algorithm for a Special Class of Trinomials},
      howpublished = {Cryptology ePrint Archive, Paper 2006/035},
      year = {2006},
      note = {\url{}},
      url = {}
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