Arithmetic on superelliptic 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 کاملRational points on Erdős–Selfridge superelliptic curves
Given k > 2, we show that there are at most finitely many rational numbers x and y 6= 0 and integers ` > 2 (with (k, `) 6= (2, 2)) for which x(x+ 1) · · · (x+ k − 1) = y. In particular, if we assume that ` is prime, then all such triples (x, y, `) satisfy either y = 0 or ` < exp(3k).
متن کاملQuantum codes from superelliptic curves
Let X be an algebraic curve of genus g ≥ 2 defined over a field Fq of characteristic p > 0. From X , under certain conditions, we can construct an algebraic geometry code CX . When this code (or its dual) is self-orthogonal under the symplectic product, a quantum algebraic geometry code QX is constructed. In this paper we study the construction of such codes from curves with automorphisms and t...
متن کاملHigher-order Weierstrass Weights of Branch Points on Superelliptic Curves
In this paper we consider the problem of calculating the higherorder Weierstrass weight of the branch points of a superelliptic curve C. For any q > 1, we give an exact formula for the q-weight of an affine branch point. We also find a formula for the q-weight of a point at infinity in the case where n and d are relatively prime. With these formulas, for any fixed n, we obtain an asymptotic for...
متن کاملThe arithmetic of Jacobian groups of superelliptic cubics
We present two algorithms for the arithmetic of cubic curves with a totally ramified prime at infinity. The first algorithm, inspired by Cantor’s reduction for hyperelliptic curves, is easily implemented with a few lines of code, making use of a polynomial arithmetic package. We prove explicit reducedness criteria for superelliptic curves of genus 3 and 4, which show the correctness of the algo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2000
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-00-01297-7