Fast arithmetic for characteristic three finite fields is desirable in pairing-based cryptography
because there is a suitable family of elliptic curves over having embedding degree 6. In this …

In this paper, we present a new cube root algorithm in the finite field F _ q F q with q qa
power of prime, which extends the Cipolla–Lehmer type algorithms (Cipolla, Un metodo per …

We present a method for computing p th roots using a polynomial basis over finite
fields\mathbb F_q of odd characteristic p, p≥ 5, by taking advantage of a binomial reduction …

We present low complexity formulae for the computation of cubing and cube root over IF 3 m
constructed using special classes of irreducible trinomials, tetranomials and pentanomials …

We discuss a family of irreducible polynomials that can be used to speed up square root
extraction in fields of characteristic two. They generalize trinomials discussed by Fong et …

A series of recent algorithmic advances has delivered highly effective methods for pairing
evaluation and parameter generation. However, the resulting multitude of options means …

The main objectives of our paper were to establish a general formula to find the cube and
higher order roots of real number using long division method. This is simultaneously …

SK Padhan, S. Gadtia, AK Pattanaik abstract: The existence as well as the computation of
roots appears in number theory, algebra, numerical analysis and other areas. The present …

The existence of computer arithmetic principles and performing different operations, like
addition, multiplication, division, squaring, cubing, extractions of square root, cube root, etc …

Решение уравнений степени не выше четырех в поле $ GF (p^ s), $ где $ p> 3$, $ s= 2^
kr, $$ k\rightarrow\infty, $$ r=\pm1\pmod6, $$ p, r= O (1) $, при использовании …