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Symmetry Arguments for Edwards Elliptic Curves

Mathematics
We revisit Edwards normal form for elliptic curves, and show how elementary symmetry arguments lead to a more general expression for his addition formula on these curves.
Stephen Andryc, Joel Langer
doaj   +1 more source

Methods for using elliptic curves in cryptography [PDF]

E3S Web of Conferences
Elliptic Curve Cryptography (ECC), a significant modern cryptography, is more secure and robust than most others due to its construction using an elliptic curve and the application of mathematical operations for encryption and key generation. Furthermore,
Obukhov Vadim, Qadamova Zulayho, Sobirov Muzaffar, Ergashev Otabek, Nabijonov Ravshanbek   +4 more
doaj   +1 more source

A Novel Image Encryption Scheme Based on Elliptic Curves over Finite Rings. [PDF]

Entropy (Basel), 2022
Hayat U, Ullah I, Azam NA, Azhar S.
europepmc   +1 more source

High-Performance Elliptic Curve Cryptography: A SIMD Approach to Modern Curves (Extended Thesis Summary)

CLEI Electronic Journal
Cryptography based on elliptic curves is endowed with efficient methods for public-key cryptography. Recent research has shown the superiority of the Montgomery and Edwards curves over the Weierstrass curves as they require fewer arithmetic operations ...
Armando Faz Hernandez, Julio López
doaj   +1 more source

Quantum Circuit Optimization for Solving Discrete Logarithm of Binary Elliptic Curves Obeying the Nearest-Neighbor Constrained. [PDF]

Entropy (Basel), 2022
Liu J, Wang H, Ma Z, Duan Q, Fei Y, Meng X.   +5 more
europepmc   +1 more source

Safe curves for elliptic-curve cryptography

This paper surveys interactions between choices of elliptic curves and the security of elliptic-curve cryptography. Attacks considered include not just discrete-logarithm computations but also attacks exploiting common implementation pitfalls.
Bernstein, Daniel J., Lange, Tanja
openaire   +2 more sources

Mestre's Finite Field Method for Searching Elliptic Curves with High Ranks

Journal of New Theory
The theory of elliptic curves is one of the popular topics of recent times with its unsolved problems and interesting conjectures. In 1922, Mordell proved that the group of $\mathbb{Q}$-rational points on an elliptic curve is finitely generated ...
Şeyda Dalkılıç, Ercan Altınışık
doaj   +1 more source

Groups of generalized G‐type and applications to torsion subgroups of rational elliptic curves over infinite extensions of Q

Transactions of the London Mathematical Society, 2019
Recently, there has been much interest in studying the torsion subgroups of elliptic curves base‐extended to infinite extensions of Q. In this paper, given a finite group G, we study what happens with the torsion of an elliptic curve E over Q when ...
Harris B. Daniels, Maarten Derickx, Jeffrey Hatley   +2 more
doaj   +1 more source

Higher-rank zeta functions for elliptic curves. [PDF]

Proc Natl Acad Sci U S A, 2020
Weng L, Zagier D.
europepmc   +1 more source