Results 51 to 60 of about 4,819,653 (62)

Cycles in the Supersingular ℓ-Isogeny Graph and Corresponding Endomorphisms

Association for Women in Mathematics Series, 2018
We study the problem of generating the endomorphism ring of a supersingular elliptic curve by two cycles in l-isogeny graphs. We prove a necessary and sufficient condition for the two endomorphisms corresponding to two cycles to be linearly independent ...
Efrat Bank, Catalina Camacho-Navarro, Kirsten Eisentraeger, T. Morrison, Jennifer Park   +4 more
semanticscholar   +1 more source

(Deep) Learning about Elliptic Curve Cryptography

IACR Cryptology ePrint Archive
: Motivated by the interest in elliptic curves both from a theoretical (algebraic geometry) and applied (cryptography) perspective, we conduct a preliminary study on the underlying mathematical structure of these mathematical structures.
Diana Maimuţ, A. Matei, George Teşeleanu   +2 more
semanticscholar   +1 more source

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

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

Construction of Secure Random Curves of Genus 2 over Prime Fields

International Conference on the Theory and Application of Cryptographic Techniques, 2004
P. Gaudry, É. Schost
semanticscholar   +1 more source

Schoof's algorithm: Point counting on elliptic curves

, 2020
Jacobus Visser
openalex  

Constructing Elliptic Curve Cryptosystems in Characteristic 2

Annual International Cryptology Conference, 1990
N. Koblitz
semanticscholar   +1 more source

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

, 2006
John J. McGee
openalex  

Counting Points on Elliptic Curves Over F2m

, 1993
A. Menezes, S. Vanstone, R. Zuccherato
semanticscholar   +1 more source

"Efficient Implementation of Schoof's Algorithm," ASIACRYPT'98

, 1998
T. Izu
openalex