Results 141 to 150 of about 38,603 (168)

Supersingular elliptic curves

, 2023
openaire   +1 more source

The main conjecture for CM elliptic curves at supersingular primes

, 2005
Robert Pollack, Karl Rubin
openalex   +2 more sources

On the modularity of supersingular elliptic curves over certain totally real number fields

, 2007
Frazer Jarvis, Jayanta Manoharmayum
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Isogenies of supersingular elliptic curves over finite fields and operations in elliptic cohomology

, 2007
Andrew Baker
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Computational problems in supersingular elliptic curve isogenies

Quantum Information Processing, 2018
We present an overview of supersingular isogeny cryptography and how it fits into the broad theme of post-quantum public-key crypto. The paper also gives a brief tutorial of elliptic curve isogenies and the computational problems relevant for supersingular isogeny crypto.
S. Galbraith, F. Vercauteren
semanticscholar   +3 more sources

On supersingular primes of the Elkies' elliptic curve

Functiones et Approximatio Commentarii Mathematici, 2018
Let $E$ be the elliptic curve $y^2=x^3+(i-2)x^2+x$ over the imaginary quadratic field $\mathbb{Q}(i)$. In this paper, we investigate the supersingular primes of $E$. We introduce the curve $C$ of genus two over $\mathbb{Q}$ covering a quotient of $E$ and for any prime number $p$, we state a condition (over $\mathbb{F}_p$) about the reduction of the ...
N. Murabayashi
semanticscholar   +4 more sources

Adding Level Structure to Supersingular Elliptic Curve Isogeny Graphs

Journal de Théorie des Nombres de Bordeaux, 2022
In this paper, we add the information of level structure to supersingular elliptic curves and study these objects with the motivation of isogeny-based cryptography.
Sarah Arpin
semanticscholar   +1 more source

Arithmetic Circuit Homomorphic Encryption Key Pairing Comparisons and Analysis between Elliptic Curve Diffie Hellman and Supersingular Isogeny Diffie Hellman

2021 2nd Asia Conference on Computers and Communications (ACCC), 2021
This project is an extension of ongoing research on Fully Homomorphic Encryption - Arithmetic Circuit Homomorphic Encryption. This paper focus on the implementation of pairing algorithm Supersingular Isogeny Diffie Hellman Key Exchange into Arithmetic ...
Wen Xin Khoo Joshua, Xin Wei Teoh Justin, C. Yap   +2 more
semanticscholar   +1 more source

Selmer groups of supersingular elliptic curves [PDF]

Journal of Soviet Mathematics, 1987
Translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 75, 16-21 (Russian) (1978; Zbl 0449.14009).
M. I. Bashmakov, A. S. Kurochkin
openaire   +2 more sources

Supersingular elliptic curves over ℤ𝑝-extensions

Journal für die Reine und Angewandte Mathematik, 2023
Let E / Q \mathrm{E}/\mathbb{Q} be an elliptic curve and 𝑝 a prime of supersingular reduction for E \mathrm{E} . Consider a quadratic extension L / Q p L/\mathbb{Q}_{p} and the corresponding anticyclotomic Z p \mathbb{Z}_{p} -extension L ∞ / L L_{\infty}/
M. Çiperiani
semanticscholar   +1 more source