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Efficient Isogeny Proofs Using Generic Techniques [PDF]

open access: yesLecture Notes in Computer Science, 2023
Generating supersingular elliptic curves of unknown endomorphism ring has been a problem vexing isogeny-based cryptographers for several years. A recent development has proposed a trusted setup protocol to generate such a curve, where each participant ...
Kelong Cong, Yi-Fu Lai, Shai Levin
exaly   +2 more sources

Unconditional Foundations for Supersingular Isogeny-Based Cryptography [PDF]

open access: yesLecture Notes in Computer Science
In this paper, we prove that the supersingular isogeny problem (Isogeny), endomorphism ring problem (EndRing) and maximal order problem (MaxOrder) are equivalent under probabilistic polynomial time reductions, unconditionally.
Benjamin Wesolowski
exaly   +3 more sources

Horizontal isogeny theorems

form, 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
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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

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