Related papers: Pairings on hyperelliptic curves
In 1986 Victor Miller described an algorithm for computing the Weil pairing in his unpublished manuscript. This algorithm has then become the core of all pairing-based cryptosystems. Many improvements of the algorithm have been presented.…
The concept of spatial coupling is among the most significant breakthroughs in coding theory over the past decade. The excellent waterfall and error floor performance of spatially coupled codes has positioned them as promising coding…
We consider the maximum chromatic number of hypergraphs consisting of cliques that have pairwise small intersections. Designs of the appropriate parameters produce optimal constructions, but these are known to exist only when the number of…
We study the approximability of an existing framework for clustering edge-colored hypergraphs, which is closely related to chromatic correlation clustering and is motivated by machine learning and data mining applications where the goal is…
In this article, we construct algebraic equations for a curve C and a map f to an elliptic curve E, with pre-specified branching data. We do this by determining certain relations that the periods of C and E must satisfy and use these…
We prove that computing a single pair of vertices that are mapped onto each other by an isomorphism $\phi$ between two isomorphic graphs is as hard as computing $\phi$ itself. This result optimally improves upon a result of G\'{a}l et al.…
We present a deterministic and explicit algorithm to compute the endomorphism rings of supersingular elliptic curves. As an example we compute the endomorphism rings of all supersingular elliptic curves defined over characteristic…
Envelopes of parameterized families of plane curves is an important topic, both for the mathematics involved and for its applications. Nowadays, it is generally studied in a technology-rich environment, and automated methods are developed…
Stratified digraphs are popular models for feedforward neural networks. However, computation of their path homologies has been limited to low dimensions due to high computational complexity. A recursive algorithm is proposed to compute…
We show how to speed up the computation of isomorphisms of hyperelliptic curves by using covariants. We also obtain new theoretical and practical results concerning models of these curves over their field of moduli.
Several problems which could be thought of as belonging to recreational mathematics are described. They are all such that solutions to the problem depend on finding rational points on elliptic curves. Many of the problems considered lead to…
We study a popular algorithm for fitting polynomial curves to scattered data based on the least squares with gradient weights. We show that sometimes this algorithm admits a substantial reduction of complexity, and, furthermore, find…
We design a probabilistic algorithm for computing endomorphism rings of ordinary elliptic curves defined over finite fields that we prove has a subexponential runtime in the size of the base field, assuming solely the generalized Riemann…
We give the complete list of possible torsion subgroups of elliptic curves with complex multiplication over number fields of degree 1-13. Additionally we describe the algorithm used to compute these torsion subgroups and its implementation.
A general scheme for determining and studying integrable deformations of algebraic curves is presented. The method is illustrated with the analysis of the hyperelliptic case. An associated multi-Hamiltonian hierarchy of systems of…
We classify completely the intersections of the Hermitian curve with parabolas in the affine plane. To obtain our results we employ well-known algebraic methods for finite fields and geometric properties of the curve automorphisms. In…
In this paper we shall give formulas for the pairings of intersection cohomology classes of complementary dimensions in the intersection cohomology of geometric invariant theoretic quotients for which semistability is not necessarily the…
We propose to study maximum flow problems for connectome graphs. We suggest a few computational problems: finding vertex pairs with maximal flow, finding new edges which would increase the maximal flow. Initial computation results for some…
This paper presents a new approach to combine cross-correlation functions. The combination is based on a maximum-likelihood approach and uses a non-linear combination scheme. It can be effective for radial-velocity analysis of multi-order…
In this paper we construct parameterizations of elliptic curves over the rationals which have many consecutive integral multiples. Using these parameterizations, we perform searches in GMP and Magma to find curves with points of small…