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On the global distance between two algebraic points on a curve

✍ Scribed by Michel Laurent; Dimitrios Poulakis

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
455 KB
Volume
104
Category
Article
ISSN
0022-314X

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✦ Synopsis

We prove diophantine inequalities involving various distances between two distinct algebraic points of an algebraic curve. These estimates may be viewed as extensions of classical Liouville's inequality. Our approach is based on a transcendental construction using algebraic functions. Next we apply our results to Hilbert's irreducibility Theorem and to some classes of diophantine equations in the circle of Runge's method.

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We consider how a linear condition on the bits representing an x-coordinate of a point on an elliptic curve over a field of characteristic two can lead to problems both in elliptic curve based Diffie-Hellman key agreement and the method of distinguished points for solving the elliptic curve discrete