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

Itoh - Tsujii Inversion in Standard Basis and Its Appli

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 ...

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

Field inversion in F2m dominates the cost of modern software implementations of certain elliptic curve cryptographic operations, such as point encoding/hashing into elliptic curves. [7, 6, 2] Itoh–Tsujii inversion using a polynomial basis and precomputed table-based multi-squaring has been demonstrated to be highly effective for software implementations [19, 14, 2], but the performance and memo...

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 ...

Quantum binary field inversion: improved circuit depth via choice of basis representation

Finite fields of the form F2m play an important role in coding theory and cryptography. We show that the choice of how to represent the elements of these fields can have a significant impact on the resource requirements for quantum arithmetic. In particular, we show how the use of Gaussian normal basis representations and of ‘ghost-bit basis’ representations can be used to implement inverters w...