Results 21 to 30 of about 2,536,804 (344)
Elliptic curve cryptography [PDF]
Ubiquity, 2008 This paper describes the Elliptic Curve Cryptography algorithm and its suitability for smart cards.
Vivek Kapoor +2 more
openaire +2 more sources
Generalized Fibonacci Sequences for Elliptic Curve Cryptography
Mathematics, 2023 The Fibonacci sequence is a well-known sequence of numbers with numerous applications in mathematics, computer science, and other fields. In recent years, there has been growing interest in studying Fibonacci-like sequences on elliptic curves.
Zakariae Cheddour +2 more
doaj +1 more source
Concrete quantum cryptanalysis of binary elliptic curves
IACR Cryptology ePrint Archive, 2020 This paper analyzes and optimizes quantum circuits for computing discrete logarithms on binary elliptic curves, including reversible circuits for fixed-base-point scalar multiplication and the full stack of relevant subroutines.
Gustavo Banegas +3 more
semanticscholar +1 more source
Regulators of Elliptic Curves [PDF]
International Mathematics Research Notices, 2018 Abstract We study the regulator of the Mordell–Weil group of elliptic curves over number fields, functions fields of characteristic 0 or function fields of characteristic $p>0$. We prove a new Northcott property for the regulator of elliptic curves of rank at least 4 defined over a number field.
Autissier, Pascal +2 more
openaire +5 more sources
Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: general formalism [PDF]
Journal of High Energy Physics, 2017 We introduce a class of iterated integrals, defined through a set of linearly independent integration kernels on elliptic curves. As a direct generalisation of multiple polylogarithms, we construct our set of integration kernels ensuring that they have ...
Johannes Broedel +3 more
semanticscholar +1 more source
Elliptic curves and the congruent number problem [PDF]
, 2023 openIn this thesis we will introduce some basic notions on the arithmetic theory of elliptic curves and show how this theory is connected to the congruent number problem, a classical problem in arithmetic.
BARBAN, FRANCESCO
core
Elliptic polylogarithms and iterated integrals on elliptic curves. II. An application to the sunrise integral [PDF]
Physical Review D, 2017 We introduce a class of iterated integrals that generalize multiple polylogarithms to elliptic curves. These elliptic multiple polylogarithms are closely related to similar functions defined in pure math- ematics and string theory.
Johannes Broedel +3 more
semanticscholar +1 more source
Preprint: Murmurations of Elliptic Curves
, 2022 We investigate the average value of the pth Dirichlet coefficients of elliptic curves for a prime p in a fixed conductor range with given rank. Plotting this average yields a striking oscillating pattern, the details of which vary with the rank. Based on
Oliver, T. +3 more
core +1 more source
Elliptic curves over totally real cubic fields are modular [PDF]
, 2019 We prove that all elliptic curves defined over totally real cubic fields are modular. This builds on previous work of Freitas, Le Hung and Siksek, who proved modularity of elliptic curves over real quadratic fields, as well as recent breakthroughs due to
M. Derickx, Filip Najman, S. Siksek
semanticscholar +1 more source
Upper bound for the height of S-integral points on elliptic curves [PDF]
, 2013 We establish new upper bounds for the height of the S-integral points of an elliptic curve. This bound is explicitly given in terms of the set $S$ of places of the number field K involved,but also in terms of the degree of K, as well as the rank, the ...
Surroca, Andrea +3 more
core +1 more source