Optimal software-implemented Itoh-Tsujii inversion for GF(2m)

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 overGF(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, withm and ...

A Fast Algorithm for Multiplicative Inversion in GF(2m) Using Normal Basis

ÐA fast algorithm for multiplicative inversion in GF …2m† using normal basis is proposed. It is an improvement on those proposed by Itoh and Tsujii and by Chang et al., which are based on Fermat's Theorem and require O…logm† multiplications. The number of multiplications is reduced by decomposing mÿ 1 into several factors and a small remainder. Index TermsÐFinite field, finite field inversion, ...

Itoh-Tsujii Inversion in Standard Basis and Its Application in Cryptography and Codes

This contribution is concerned with a generalization of Itoh and Tsujii’s algorithm for inversion in extension fields GF (q). Unlike the original algorithm, the method introduced here uses a standard (or polynomial) basis representation. The inversion method is generalized for standard basis representation and relevant complexity expressions are established, consisting of the number of extensio...

Itoh - Tsujii Inversion in Standard Basis and Its Appli

Optimal Extension Field Inversion in the Frequency Domain

In this paper, we propose an adaptation of the Itoh-Tsujii algorithm to the frequency domain for efficient inversion in a class of Optimal Extension Fields. To the best of our knowledge, this is the first time a frequency domain finite field inversion algorithm is proposed for elliptic curve cryptography. We believe the proposed algorithm would be well suited especially for efficient low-power ...