Itoh–Tsujii Inversion Algorithm

^∗Work done while the author was at Philips Research, The Netherlands

Definition

Originally introduced in [5], the Itoh and Tsujii algorithm (ITA) is an exponentiation-based algorithm for inversion in finite fields which reduces the complexity of computing the inverse of a nonzero element in ${\mathbb{F}}_{{2}^{n}}$, when using a normal basis representation, from n − 2 multiplications in ${\mathbb{F}}_{{2}^{n}}$ and n − 1 cyclic shifts using the binary exponentiation method to at most $2{\lfloor \log }_{2}(n - 1)\rfloor$ multiplications in ${\mathbb{F}}_{{2}^{n}}$ and n − 1 cyclic shifts. As shown in [4], the method is also applicable to finite fields with a polynomial basis representation.

Related Concepts

It is a well-known fact that there are several possibilities to represent elements of a finite field. In particular, given an irreducible polynomial P(x) of degree m over ${\mathbb{F}}_{q}$ and a root $\alpha$ of P(x) (i.e., $P(\alpha ) = 0$), one can represent an...