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Showing 1 to 13 of 13 for “"Hyperelliptic curves"”.
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Rigid Analytic Uniformization of Hyperelliptic Curves
… curve model O/Gamma of a given totally split hyperelliptic curve y2 = i=12g+2x-a i . Once the generators of the Schottky group Gamma are obtained, we also explain how to use them to compute the period lattice of the Jacobian of the curve.
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On the Orders of Jacobians of Hyperelliptic Curves
… perform group operations in Jacobians of hyperelliptic curves and methods of finding their orders. We conclude by generalizing some heuristics from the case of genus 1 to genus 2 and beyond.
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Coleman integration for hyperelliptic curves : algorithms and applications
… algorithms for computing Coleman integrals on hyperelliptic curves and discuss some immediate applications. I give algorithms to compute single and iterated integrals on odd models of hyperelliptic curves, as well as the necessary modifications to iplemieit these algorithms for even models. …
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The Arithmetic of Elliptic and Hyperelliptic Curves with Applications to Pairing-Based Cryptography
… extensive treatment of the theory of algebraic curves and their connection to the theory of algebraic function fields of one variable, the thesis concentrates on pairings (such as the Tate pairing) defined on groups related to a given absolutely irreducible non-singular curve over a finite …
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SEMISTABLE MODELS OF HYPERELLIPTIC CURVES IN THE WILD CASE & DIFFERENTIAL OPERATORS ON P-ADIC MODULAR FORMS
… with J. Yelton, regarding semistable models of hyperelliptic curves in the wild case. To this subject, which was already the topic of my MSc. thesis, I devoted part of my research work during my PhD, until completing it during summer 2022. The second part of this thesis discusses some research …
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Constructing suitable ordinary pairing-friendly curves: A case of elliptic curves and genus two hyperelliptic curves
… is to construct suitable pairing-friendly curves: Curves which would provide e�cient implementation without compromising the security of the protocols. These curves have small embedding degree and large prime order subgroup. Random curves are likely to have large embedding degree and hence …
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Point Counting On Genus 2 Curves
… points on the jacobian variety of a given hyperelliptic curve is of great importance. There has been several approaches to obtain the cardinality of such a group, specially for hyperelliptic curves of genus 2. The best known algorithm for counting points on genus 2 curves over prime fields …
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Invariants linked to models of curves over discrete valuation rings
… conductor and the minimal discriminant of a hyperelliptic curve defined over the fraction field K of a discrete valuation ring. The Artin conductor and the minimal discriminant are two measures of degeneracy of the singular fiber in a family of hyperelliptic curves. In the case of elliptic …
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Excess Porteous, Coherent Porteous, and the Hyperelliptic Locus in M3
In the moduli space of curves of genus 3, the locus of hyperelliptic curves forms a divisor, that is a closed subscheme of codimension 1. J. Harris and I. Morrison compute an expression for the class of this divisor, in the Chow ring of the moduli space, using a map of vector bundles and by …
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Algebraic Curves Over Supersimple Fields
In this work we are concerned with algebraic curves over supersimple fields. First it is proved that an elliptic curve defined over a supersimple field K whose j-invariant is s-generic over empty has a rational point over K which is s-generic over the set of parameters used to define the curve. …
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Explicit division and torsion points on superelliptic Curves and jacobians
… two problems in the arithmetic of superelliptic curves. By a superelliptic curve, I mean the smooth projective model of the affine plane curve y[superscript n] = f(x) where f(x) is separable, n is coprime to deg(f), and the characteristic of the ground field does not divide n. When n = 2, this is …
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Minimum distance of error correcting codes versus encoding complexity, symmetry, and pseudorandomness
… are in one-to-one correspondence with special hyperelliptic curves over a finite field of prime order where the number of zeros of a codeword corresponds to the number of rational points.
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Computing canonical heights on Jacobians
… heights on Jacobians of smooth projective curves. Building on an existing algorithm due to Flynn and Smart with modifications by Stoll we generalize efficient methods for the computation of canonical heights on elliptic curves to the case of Jacobian surfaces. The main tools are the …