Software implementation of arithmetic in
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 …
because there is a suitable family of elliptic curves over having embedding degree 6. In this …
New cube root algorithm based on the third order linear recurrence relations in finite fields
GH Cho, N Koo, E Ha, S Kwon - Designs, Codes and Cryptography, 2015 - Springer
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 …
power of prime, which extends the Cipolla–Lehmer type algorithms (Cipolla, Un metodo per …
Efficient pth root computations in finite fields of characteristic p
D Panario, D Thomson - Designs, Codes and Cryptography, 2009 - Springer
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 …
fields\mathbb F_q of odd characteristic p, p≥ 5, by taking advantage of a binomial reduction …
Low Complexity Cubing and Cube Root Computation over $\F_ {3^ m} $ in Polynomial Basis
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 …
constructed using special classes of irreducible trinomials, tetranomials and pentanomials …
Another look at square roots (and other less common operations) in fields of even characteristic
RM Avanzi - Selected Areas in Cryptography: 14th International …, 2007 - Springer
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 …
extraction in fields of characteristic two. They generalize trinomials discussed by Fong et …
[HTML][HTML] FPGA based implementation for extracting the roots of real number
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 …
higher order roots of real number using long division method. This is simultaneously …
Instruction set extensions for pairing-based cryptography
A series of recent algorithmic advances has delivered highly effective methods for pairing
evaluation and parameter generation. However, the resulting multitude of options means …
evaluation and parameter generation. However, the resulting multitude of options means …
[PDF][PDF] Remarks on Heron's cubic root iteration formula
SK Padhan, S Gadtia, AK Pattanaik - Boletim da Sociedade …, 2017 - academia.edu
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 …
roots appears in number theory, algebra, numerical analysis and other areas. The present …
Another look at square roots and traces (and quadratic equations) in fields of even characteristic
R Avanzi - Cryptology ePrint Archive, 2007 - eprint.iacr.org
We discuss irreducible polynomials that can be used to speed up square root extraction in
fields of characteristic two. We call such polynomials\textit {square root friendly}. The obvious …
fields of characteristic two. We call such polynomials\textit {square root friendly}. The obvious …
An Organized Literature Review on Various Cubic Root Algorithmic Practices for Develo** Efficient VLSI Computing System—Understanding Complexity
SK Panda, K Achyut, SK Kulkarni… - Artificial Intelligence …, 2023 - Wiley Online Library
The existence of computer arithmetic principles and performing different operations, like
addition, multiplication, division, squaring, cubing, extractions of square root, cube root, etc …
addition, multiplication, division, squaring, cubing, extractions of square root, cube root, etc …