Results 91 to 100 of about 6,909,811 (176)

Group structure of elliptic curves over ℤ/Nℤ

Journal of Mathematical Cryptology
We characterize the possible groups E(Z∕NZ)E\left({\mathbb{Z}}/N{\mathbb{Z}}) arising from elliptic curves over Z∕NZ{\mathbb{Z}}/N{\mathbb{Z}} in terms of the groups E(Fp)E\left({{\mathbb{F}}}_{p}), with pp varying among the prime divisors of NN.
Sala Massimiliano, Taufer Daniele
doaj   +1 more source

Direct Construction of Quantized Tensor Trains With Small Rank for Laplace‐ or Gaussian‐Transformed Analytic Functions

International Journal for Numerical Methods in Engineering, Volume 127, Issue 18, 30 September 2026.
ABSTRACT Preparing quantum states with desired amplitude distributions is a key bottleneck in the implementation of quantum linear and nonlinear dynamics solvers, including Linear Combination of Hamiltonian Simulation (LCHS) and Schrödingerization. We present a direct, closed‐form construction of Quantized Tensor Train (QTT) representations for two ...
Katsuhiro Endo, Kazuaki Z. Takahashi
wiley   +1 more source

Polynomial interpolation of the elliptic curve and XTR discrete logarithm

, 2002
We prove lower bounds on the degree of polynomials interpolating the discrete logarithm in the group of points on an elliptic curve over a finite field and the XTR discrete logarithm ...
Lange, T., Winterhof, A., Tanja Lange, Arne Winterhof, Lange, T Tanja, Winterhof, A   +5 more
core   +1 more source

Hybrid Coupling With Operator Inference and the Overlapping Schwarz Alternating Method

International Journal for Numerical Methods in Engineering, Volume 127, Issue 17, 15 September 2026.
ABSTRACT This paper presents a hybrid approach for coupling subdomain‐local, nonintrusive Operator Inference (OpInf) reduced order models (ROMs) with each other and with subdomain‐local, high‐fidelity full order models (FOMs) using the overlapping Schwarz alternating method (O‐SAM).
Irina Tezaur, Eric Parish, Anthony Gruber, Ian Moore, Christopher Wentland, Alejandro Mota   +5 more
wiley   +1 more source

Index Calculus for Abelian Varieties and the Elliptic Curve Discrete Logarithm Problem

, 2004
We propose an index calculus algorithm for the discrete logarithm problem on general abelian varieties. The main difference with the previous approaches is that we do not make use of any embedding into the Jacobian of a well-suited curve.
Pierrick Gaudry
core   +1 more source

Two-party Authenticated Multiple-key Agreement Based on Elliptic Curve Discrete Logarithm Problem

, 2013
[[abstract]]In this paper, we propose a protocol to generate n 2 keys in one session under the assumption of the intractability of the elliptic curve discrete logarithm problem and MQV protocol.
Huan, Li-Chin;Huang, Li-Chin;黃明祥;Hwang, Min-Shiang
core  

Lifting Elliptic Curves and Solving the Elliptic Curve Discrete Logarithm Problem

, 2000
Essentially all subexponential time algorithms for the discrete logarithm problem over finite fields are based on the index calculus idea. In proposing cryptosystems based on the elliptic curve discrete logarithm problem (ECDLP) Miller [6] also gave ...
Ka Lam Kueh, Ming-deh A. Huang, Ki-Seng Tan   +2 more
core   +1 more source

A New Anonymous Conference Key Distribution System Based on the Elliptic Curve Discrete Logarithm Problem

, 2012
[[abstract]]In 1999, Tseng and Jan [Comput. Commun. 22 (1999) 749] proposed two conference key distribution systems (CKDS) with user anonymity based on the discrete logarithm problem and the interpolating properties of polynomials.
黃明祥;Hwang, Min-Shiang
core  

A New Method for Geometric Interpretation of Elliptic Curve Discrete Logarithm Problem [PDF]

, 2019
In this paper, we intend to study the geometric meaning of the discrete logarithm problem defined over an Elliptic Curve. The key idea is to reduce the Elliptic Curve Discrete Logarithm Problem (EC-DLP) into a system of equations.
Daniele Di Tullio, Ankan Pal
core   +1 more source

The Elliptic Curve Discrete Logarithm and Functional Graphs [PDF]

, 2011
The discrete logarithm problem, and its adaptation to elliptic curves, called the elliptic curve discrete logarithm problem (ECDLP) is an open problem in the field of number theory, and its applications to modern cryptographic algorithms are numerous ...
Evans, Christopher J
core   +1 more source