Renate Scheidler
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The Spine of a Supersingular $\ell$-Isogeny graph Open
Supersingular elliptic curve $\ell$-isogeny graphs over finite fields offer a setting for a number of quantum-resistant cryptographic protocols. The security analysis of these schemes typically assumes that these graphs behave randomly. Mo…
View article: PEARL-SCALLOP: Parameter Extension Applicable in Real Life for SCALLOP
PEARL-SCALLOP: Parameter Extension Applicable in Real Life for SCALLOP Open
A crucial ingredient for many cryptographic primitives such as key exchange protocols and advanced signature schemes is a commutative group action where the structure of the underlying group can be computed efficiently. SCALLOP provides su…
Solving norm equations in global function fields Open
We present two new algorithms for solving norm equations over global function fields with at least one infinite place of degree 1 and no wild ramification. The first of these is a substantial improvement of a method due to Gaál and Pohst, …
On invariants of Artin-Schreier curves Open
The main goal of this article is to expand the theory of invariants of Artin-Schreier curves by giving a complete classification in genus 3 and 4. To achieve this goal, we first establish standard forms of Artin-Schreier curves and determi…
Improved methods for finding imaginary quadratic fields with high 𝑛-rank Open
We describe a generalization and improvement of Diaz y Diaz’s search technique for imaginary quadratic fields with -rank at least 2, one of the most successful algorithms for generating many examples with relatively small discriminants, to…
Orienteering with One Endomorphism Open
In supersingular isogeny-based cryptography, the path-finding problem reduces to the endomorphism ring problem. Can path-finding be reduced to knowing just one endomorphism? It is known that a small degree endomorphism enables polynomial-t…
Orientations and cycles in supersingular isogeny graphs Open
The paper concerns several theoretical aspects of oriented supersingular $\ell$-isogeny volcanoes and their relationship to closed walks in the supersingular $\ell$-isogeny graph. Our main result is a bijection between the rims of the unio…
Orienteering with one endomorphism Open
In supersingular isogeny-based cryptography, the path-finding problem reduces to the endomorphism ring problem. Can path-finding be reduced to knowing just one endomorphism? It is known that a small endomorphism enables polynomial-time pat…
Divisor class group arithmetic on C3,4curves Open
We present novel explicit formulas for arithmetic in the divisor class group of a C 3,4 curve.Our formulas handle all cases of inputs and outputs without having to fall back on a generic method.We also improve on the most commonly occurrin…
Difference Necklaces Open
An $(a,b)$-difference necklace of length $n$ is a circular arrangement of the integers $0, 1, 2, \ldots , n-1$ such that any two neighbours have absolute difference $a$ or $b$. We prove that, subject to certain conditions on $a$ and $b$, s…
Preface Open
The biennial, international Algorithmic Number Theory Symposium (ANTS) provides the premier international forum for state-of-the-art research in computational and algorithmic number theory.This conference is devoted to algorithmic aspects …
A class of Artin-Schreier curves with many automorphisms Open
Algebraic curves with many points are useful in coding theory, but are also of number theoretic and geometric interest in their own right. Their symmetries are described by their automorphism group. Other information, such as the number of…
Class number and regulator computation in cubic function fields Open
We present computational results on the divisor class number and the regulator of a cubic function field over a large base field. The underlying method is based on approximations of the Euler product representation of the zeta function of …