相关论文: More constructing pairing-friendly elliptic curves…
An abundance of real-world problems manifest as covering edges and/or vertices of a graph with cliques that are optimized for some objectives. We consider different structural parameters of graph, and design fixed-parameter tractable…
We consider the problem of clustering misaligned curves. According to our similarity measure, two curves are considered similar if they have the same shape after being aligned, and the warping function does not differ from the identity…
The procedure of Least Square-Errors curve fitting is extensively used in many computer applications for fitting a polynomial curve of a given degree to approximate a set of data. Although various methodologies exist to carry out curve…
Given a prime power q, for every pair of positive integers m and n with m dividing the GCD of n and q-1, we construct a modular curve over F_q that parametrizes elliptic curves over F_q along with F_q-defined points P and Q of order m and…
We show how the Weil pairing can be used to evaluate the assigned characters of an imaginary quadratic order $\mathcal{O}$ in an unknown ideal class $[\mathfrak{a}] \in \mathrm{Cl}(\mathcal{O})$ that connects two given…
The elliptic curve discrete logarithm problem is considered a secure cryptographic primitive. The purpose of this paper is to propose a paradigm shift in attacking the elliptic curve discrete logarithm problem. In this paper, we will argue…
We consider algebraic affine and projective curves of Edwards \cite{E, SkOdProj} over a finite field $\text{F}_{p^n}$. Most cryptosystems of the modern cryptography \cite{SkBlock} can be naturally transform into elliptic curves \cite{Kob}.…
Two problems are addressed: reduction of an arbitrary degree non-special divisor to the equivalent divisor of the degree equal to genus of a curve, and addition of divisors of arbitrary degrees. The hyperelliptic case is considered as the…
Let p>3 be a prime and let E, E' be supersingular elliptic curves over F_p. We want to construct an isogeny phi: E --> E'. The currently fastest algorithm for finding isogenies between supersingular elliptic curves solves this problem by…
With the advent of machine learning and quantum computing, the 21st century has gone from a place of relative algorithmic security, to one of speculative unease and possibly, cyber catastrophe. Modern algorithms like Elliptic Curve…
Mazur and Rubin introduced the notion of $n$-Selmer companion elliptic curves and gave several examples of pairs of non-isogenous Selmer companions. We construct several pairs of families of elliptic curves, each parameterised by $t\in\ZZ$,…
I prove lower bounds of some parameters of elliptic curve over finite field. There parameters are closely interrelated with cryptographic stability of elliptic curve.
Given a pair of elliptic curves $E_1,E_2$ over a field $k$, we have a natural map $\text{CH}^1(E_1)_0\otimes\text{CH}^1(E_2)_0\to\text{CH}^2(E_1\times E_2)$, and a conjecture due to Beilinson predicts that the image of this map is finite…
In this paper, $p$ and $q$ are two different odd primes. First, We construct the congruent elliptic curves corresponding to $p$, $2p$, $pq$, and $2pq,$ then, in the cases of congruent numbers, we determine the rank of the corresponding…
We present a framework for constructing examples of smooth projective curves over number fields with explicitly given elements in their second K-group using elementary algebraic geometry. This leads to new examples for hyperelliptic curves…
Many problems in computational geometry are not stated in graph-theoretic terms, but can be solved efficiently by constructing an auxiliary graph and performing a graph-theoretic algorithm on it. Often, the efficiency of the algorithm…
Elliptic curve cryptography (ECC) is a widely established cryptographic technique, recognized for its effectiveness and reliability across a broad range of applications such as securing telecommunications or safeguarding cryptocurrency…
In this paper, we propose an elliptic curve key generation processor over GF(2m) and GF(P) with Network-on-Chip (NoC) design scheme based on binary scalar multiplication algorithm. Over the Two last decades, Elliptic Curve Cryptography…
In this paper we focus on various aspects of singular complex plane curves, mostly in the context of their homological properties and the associated combinatorial structures. We formulate some challenging open problems that can point to new…
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…