Results 61 to 70 of about 124 (95)

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  

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

open access: yes, 2006
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
McGee, John J.
core  

Symbolic method in the Schoof's algorithm

open access: yes
Głównym tematem pracy jest przedstawienie algorytmu Schoofa w kontekście szczególnych przypadków krzywej eliptycznej nad ciałem skończonym. Praca została podzielona na trzy rozdziały.
Asienkiewicz, Hubert
core  

Primality proving with cyclotomy [PDF]

open access: yes, 1990
Bosma, W. (Wieb)   +1 more
core  

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
openaire   +1 more source

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.
Tetsuya Izu   +3 more
openaire   +1 more source

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