相关论文: Optimal Ate Pairing on Elliptic Curves with Embedd…

Finite difference methods (FDMs) are widely used for solving partial differential equations (PDEs) due to their relatively simple implementation. However, they face significant challenges when applied to non-rectangular domains and in…

Let $E$ be an elliptic curve over a number field $K$. Descent calculations on $E$ can be used to find upper bounds for the rank of the Mordell-Weil group, and to compute covering curves that assist in the search for generators of this…

In modern critical infrastructure such as power grids, it is crucial to ensure security of data communications between network-connected devices while following strict latency criteria. This necessitates the use of cryptographic hardware…

We provide a natural definition of an elliptic arrangement, extending the classical framework to an elliptic curve E with complex multiplication. We analyse the intersections of elements of the arrangement and their connected components as…

We introduce a new numerical method based on machine learning to approximate the solution of elliptic partial differential equations with collocation using a set of sigmoidal functions. We show that a feedforward neural network with a…

We compute equations for the families of elliptic curves 9-congruent to a given elliptic curve. We use these to find infinitely many non-trivial pairs of 9-congruent elliptic curves over Q, i.e. pairs of non-isogenous elliptic curves over Q…

This paper introduces the \emph{$d$-distance $b$-matching problem}, in which we are given a bipartite graph $G=(S,T;E)$ with $S=\{s_1,\dots,s_n\}$, a weight function on the edges, an integer $d\in\mathbb{Z}_+$ and a degree bound function…

This paper introduces Elliptic Curve Modulation (ECM), a novel modulation scheme that can be leveraged to effectively shuffle transmitted data while maintaining symbol error probability (SEP) performance equivalent to unencrypted systems.…

Cat qubits provide appealing building blocks for quantum computing. They exhibit a tunable noise bias yielding an exponential suppression of bit flips with the average photon number and a protection against the remaining phase errors can be…

Efficient scalar multiplication in Abelian groups (which is an important operation in public key cryptography) can be performed using digital expansions. Apart from rational integer bases (double-and-add algorithm), imaginary quadratic…

For positive rank $r$ elliptic curves $E(\mathbb{Q})$, we employ ideal class pairings $$ E(\mathbb{Q})\times E_{-D}(\mathbb{Q}) \rightarrow \mathrm{CL}(-D), $$ for quadratic twists $E_{-D}(\mathbb{Q})$ with a suitable ``small $y$-height''…

We propose an efficient and easy-to-implement gradient-enhanced least squares Monte Carlo method for computing price and Greeks (i.e., derivatives of the price function) of high-dimensional American options. It employs the sparse Hermite…

Specific quantum algorithms exist to-in theory-break elliptic curve cryptographic protocols. Implementing these algorithms requires designing quantum circuits that perform elliptic curve arithmetic. To accurately judge a cryptographic…

The determination of the maximal length of maximum distance separable (MDS) codes arising from elliptic curves is a central problem in coding theory. For an elliptic curve $E$ over $\mathbb{F}_q$, let $\operatorname{MEC}(k,q)$ denote the…

In this paper, we introduce a multiscale framework based on adaptive edge basis functions to solve second-order linear elliptic PDEs with rough coefficients. One of the main results is that we prove the proposed multiscale method achieves…

We study the convergence rate of Bregman gradient methods for convex optimization in the space of measures on a $d$-dimensional manifold. Under basic regularity assumptions, we show that the suboptimality gap at iteration $k$ is in…

In the Tree Augmentation problem we are given a tree $T=(V,F)$ and a set $E \subseteq V \times V$ of edges with positive integer costs $\{c_e:e \in E\}$. The goal is to augment $T$ by a minimum cost edge set $J \subseteq E$ such that $T…

The Discrete Logarithm Problem (DLP) for elliptic curves has been extensively studied since, for instance, it is the core of the security of cryptosystems like Elliptic Curve Cryptography (ECC). In this paper, we present an attack to the…

This thesis examines the relationship between elliptic curves with complex multiplication and Lambda structures. Our main result is to show that the moduli stack of elliptic curves with complex multiplication, and the universal elliptic…

To solve deep metric learning problems and producing feature embeddings, current methodologies will commonly use a triplet model to minimise the relative distance between samples from the same class and maximise the relative distance…