Arithmetic on curves
نویسندگان
چکیده
منابع مشابه
Arithmetic on superelliptic curves
superelliptic curves, jacobians, cryptography, discrete logarithm problem In this paper we present an efficient, polynomial-time method to perform calculations in the divisor class group of a curve which has a single point on its normalization above infinity. In particular, we provide a unique representation of divisor classes and an algorithm for reducing a divisor on such a curve to its corre...
متن کاملArithmetic progressions on Huff curves
We look at arithmetic progressions on elliptic curves known as Huff curves. By an arithmetic progression on an elliptic curve, we mean that either the x or y-coordinates of a sequence of rational points on the curve form an arithmetic progression. Previous work has found arithmetic progressions on Weierstrass curves, quartic curves, Edwards curves, and genus 2 curves. We find an infinite number...
متن کاملArithmetic Progressions on Edwards Curves
Several authors have investigated the problem of finding elliptic curves over Q that contain rational points whose x-coordinates are in arithmetic progression. Traditionally, the elliptic curve has been taken in the form of an elliptic cubic or elliptic quartic. Moody studied this question for elliptic curves in Edwards form, and showed that there are infinitely many such curves upon which ther...
متن کاملOn Arithmetic Of Hyperelliptic Curves
In this exposé, Pell’s equation is put in a geometric perspective, and a version of Artin’s primitive roots conjecture is formulated for hyperelliptic jacobians. Also explained are some recent results which throw new lights, having to do with Ankeny-Artin-Chowla’s conjecture, class number relations, and Cohen-Lenstra heuristics.
متن کاملEfficient Arithmetic on Koblitz Curves
It has become increasingly common to implement discrete-logarithm based public-key protocols on elliptic curves over finite fields. The basic operation is scalar multiplication: taking a given integer multiple of a given point on the curve. The cost of the protocols depends on that of the elliptic scalar multiplication operation. Koblitz introduced a family of curves which admit especially fast...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1986
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1986-15430-3