Results 291 to 300 of about 2,536,804 (344)
Some of the next articles are maybe not open access.
2003
The purpose of the present text is to give an elementary introduction to the arithmetic of elliptic curves over number fields from a computational point of view. This branch of number theory is particularly accessible to computer assisted calculations, and the authors make use of this feature by approaching the theory from a computational point of view.
Schmitt, S., Zimmer, H.
openaire +3 more sources
The purpose of the present text is to give an elementary introduction to the arithmetic of elliptic curves over number fields from a computational point of view. This branch of number theory is particularly accessible to computer assisted calculations, and the authors make use of this feature by approaching the theory from a computational point of view.
Schmitt, S., Zimmer, H.
openaire +3 more sources
Rasterization of elliptic curves
Computers & Graphics, 1994Abstract An algorithm for automatically rasterizing an implicitly defined curve that is based on following sign changes and which avoids gradient computations is described. The algorithm is used to visualize families of elliptic curves.
Sandy D. Balkin +2 more
openaire +1 more source
ELLIPTIC CURVES AND -ADIC ELLIPTIC TRANSCENDENCE
Bulletin of the Australian Mathematical Society, 2021AbstractWe prove a necessary and sufficient condition for isogenous elliptic curves based on the algebraic dependence ofp-adic elliptic functions. As a consequence, we give a short proof of thep-adic analogue of Schneider’s theorem on the linear independence ofp-adic elliptic logarithms of algebraic points on two nonisogenous elliptic curves defined ...
openaire +1 more source
2005
Elliptic curves constitute one of the main topics of this book. They have been proposed for applications in cryptography due to their fast group law and because so far no subexponential attack on their discrete logarithm problem (cf. Section 1.5) is known. We deal with security issues in later chapters and concentrate on the group arithmetic here.
Doche, C., Lange, T.
openaire +2 more sources
Elliptic curves constitute one of the main topics of this book. They have been proposed for applications in cryptography due to their fast group law and because so far no subexponential attack on their discrete logarithm problem (cf. Section 1.5) is known. We deal with security issues in later chapters and concentrate on the group arithmetic here.
Doche, C., Lange, T.
openaire +2 more sources
American Journal of Mathematics, 1931
Zwei ebene Kurven heißen perspektiv, wenn zwischen den Punkten der ersten und den Tangenten der zweiten eine \((1,1)\)-Korrespondenz derart hergestellt werden kann, daß jede Tangente der zweiten durch den entsprechenden Punkt der ersten läuft. So sind z. B.
openaire +2 more sources
Zwei ebene Kurven heißen perspektiv, wenn zwischen den Punkten der ersten und den Tangenten der zweiten eine \((1,1)\)-Korrespondenz derart hergestellt werden kann, daß jede Tangente der zweiten durch den entsprechenden Punkt der ersten läuft. So sind z. B.
openaire +2 more sources
Curves for the Mathematically Curious, 2019
The main focus of this paper is the study of elliptic curves, non-singular projective curves of genus 1. Under a geometric operation, the rational points E(Q) of an elliptic curve E form a group, which is a finitely-generated abelian group by Mordell’s ...
Samuel S. Wagstaff
semanticscholar +1 more source
The main focus of this paper is the study of elliptic curves, non-singular projective curves of genus 1. Under a geometric operation, the rational points E(Q) of an elliptic curve E form a group, which is a finitely-generated abelian group by Mordell’s ...
Samuel S. Wagstaff
semanticscholar +1 more source
The State of Elliptic Curve Cryptography
Designs, Codes and Cryptography, 2000This paper surveys the elliptic curve cryptography that is based on the discrete logarithm problem. Compared to their counterparts in groups of integers, elliptic curves usually provide smaller keys and lower computational complexities. The paper gives a brief overview of elliptic curves, discusses the elliptic curve discrete logarithm problem and ...
Neal Koblitz +2 more
openaire +1 more source
Elliptic Curve Paillier Schemes
Journal of Cryptology, 2002This paper is concerned with generalisations of Paillier's probabilistic encryption scheme from the integers modulo a square to elliptic curves over rings. Paillier himself described two public key encryption schemes based on anomalous elliptic curves over rings. It is argued that these schemes are not secure.
openaire +3 more sources
Elliptic Curve Cryptography Engineering
Proceedings of the IEEE, 2006In recent years, elliptic curve cryptography (ECC) has gained widespread exposure and acceptance, and has already been included in many security standards. Engineering of ECC is a complex, interdisciplinary research field encompassing such fields as mathematics, computer science, and electrical engineering.
CILARDO, Alessandro +3 more
openaire +3 more sources