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The order elliptic curves over finite fields of characteristic two using the Schoof algorithm

open access: yesThe order elliptic curves over finite fields of characteristic two using the Schoof algorithm
The elliptic curve cryptosystem is a popular cryptosystem. Its safety depends on the difficulty of the elliptic curve discrete logarithm problem (ECDLP). From the viewpoint of ECDLP, it is very interesting to determine the order of elliptic curves.
openaire  

Schoof's Algorithm and Extensions

open access: closed, 1999
Ian F. Blake   +2 more
openalex   +2 more sources

Design and Implementation of Lightweight Dynamic Elliptic Curve Cryptography Using Schoof’s Algorithm

2021
Security and efficiency for resource constrained devices using lightweight cryptography techniques is still a problem. It is important to make these devices secure from the intruders and communicate with them securely. Elliptic Curve Cryptography (ECC) comes out to be a major contender to solve this problem as it provides the security using smaller key
Ansh Tyagi   +2 more
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Parameters for secure elliptic curve cryptosystem -improvements on Schoof s algorithm

1998
The security of elliptic curve cryptosystem depends on the choice of an elliptic curve on which cryptographic operations are performed. Schoof's algorithm is used to define a secure elliptic curve, as it can compute the number of rational points on a randomly selected elliptic curve defined over a finite field.
Jun Kogure   +3 more
openaire   +2 more sources

Schoofův algoritmus pro Weierstrassovy křivky

2023
Schoof's algorithm is the starting point for the most efficient methods for determining the number of rational points on an elliptic curve defined over a finite field. The goal of this thesis is to introduce the subject of elliptic curves, with the emphasis on Weierstrass curves over a finite field, to describe Schoof's algorithm and its time ...
openaire   +1 more source

Clinical management of metastatic colorectal cancer in the era of precision medicine

Ca-A Cancer Journal for Clinicians, 2022
, Davide Ciardiello, Giulia Martini
exaly  

René Schoof's Algorithm for Determining the Order of the Group of Points on an Elliptic Curve over a Finite Field

2014
Elliptic curves have a rich mathematical history dating back to Diophantus (c. 250 C.E.), who used a form of these cubic equations to find right triangles of integer area with rational sides. In more recent times the deep mathematics of elliptic curves was used by Andrew Wiles et.
openaire   +1 more source

The Arithmetic Optimization Algorithm

Computer Methods in Applied Mechanics and Engineering, 2021
Laith Mohammad Abualigah   +2 more
exaly  

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