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Verifiable Isogeny Walks: Towards an Isogeny-Based Postquantum VDF

Lecture Notes in Computer Science, 2022
Mehdi Tibouchi   +2 more
exaly   +3 more sources

Horizontal isogeny theorems

Forum Mathematicum, 2002
Summary: Let \(K\) be a field which is finitely generated over its prime field. Consider elliptic curves \(E\) and \(E'\) defined over \(K\). Suppose there exists \(c\geq 1\) and a set \(\Lambda\) of prime numbers such that \([K(E_l,E_l'): K(E_l)\cap K(E_l')]\leq c\) for all \(l\in\Lambda\).
Frey, Gerhard, Jarden, Moshe
openaire   +2 more sources

Leveled Isogeny Problems with Hints

We define and analyze the Leveled Isogeny Problem with Hints (LIPH), which is a generalization of the Isogeny Problem with Level Structure first introduced by De Feo, Fouotsa and Panny at EUROCRYPT’24. In a LIPH instance, we are tasked to recover a secret isogeny φ$$\varphi $$ given masked torsion point images M·(φ(P),φ(Q))⊤$$M\cdot (\varphi (P ...
Subham Das   +3 more
openaire   +2 more sources

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.
openaire   +1 more source

Infinite families of isogeny-torsion graphs

Journal of Number Theory, 2023
Garen Chiloyan
exaly  

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