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Radical Isogenies and Modular Curves

Advances in Mathematics of Communications
This article explores the connection between radical isogenies and modular curves. Radical isogenies are formulas designed for the computation of chains of isogenies of fixed small degree $N$, introduced by Castryck, Decru, and Vercauteren at Asiacrypt 2020.
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The Isogeny Theorems

1987
We return to p-adic representations. Let A be an elliptic curve defined over K. We take points of A in a fixed algebraic closure Ka. We have the p-adic spaces T p (A) and V p (A) over Z p and Q p respectively.
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Verifiable Isogeny Walks: Towards an Isogeny-Based Postquantum VDF

2022
Jorge Chávez-Saab, Francisco Rodríguez-Henríquez, Mehdi Tibouchi   +2 more
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Isogeny Volcanoes and the SEA Algorithm

2002
Recently, Kohel gave algorithms to compute the conductor of the endomorphism ring of an ordinary elliptic curve, given the cardinality of the curve. Using his work, we give a complete description of the structure of curves related via rational l-degree isogenies, a structure we call a volcano.
Mireille Fouquet, François Morain
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Computing isogenies

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Radical Isogenies on Montgomery Curves

Lecture Notes in Computer Science, 2022
Hiroshi Onuki, Tomoki Moriya
exaly  

Fully Projective Radical Isogenies in Constant-Time

Lecture Notes in Computer Science, 2022
Jesus-Javier Chi-Domínguez
exaly  

SQISign: Compact Post-Quantum Signatures From Quaternions and Isogenies

Lecture Notes in Computer Science, 2020
Luca De Feo, Christophe Petit, Benjamin Wesolowski   +2 more
exaly  

Isogeny Interpolation and the Computation of Isogenies from Higher Dimensional Representations

David Jao, Jeanne Laflamme
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Computing the Height of Volcanoes of ℓ-Isogenies of Elliptic Curves Over Finite Fields

Applied Mathematics and Computation, 2008
Magda Valls, Daniel Sadornil, Josep M. Miret   +2 more
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