∗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...
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Guajardo, J. (2011). Itoh–Tsujii Inversion Algorithm. In: van Tilborg, H.C.A., Jajodia, S. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-5906-5_34
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