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Creators/Authors contains: "Jacobson, Micheal"

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  1. ; ; (, Indocrypt 2019)
    We propose a quantum algorithm for computing an isogeny between two elliptic curves E1,E2 defined over a finite field such that there is an imaginary quadratic order O satisfying O~End(Ei )for i=1,2. This concerns ordinary curves and supersingular curves defined over Fp (the latter used in the recent CSIDH proposal). Our algorithm has heuristic asymptotic run time exp(O(√log(|Δ|))) and requires polynomial quantum memory and exp(O(√log(|Δ|))) quantumly accessible classical memory, where Δ is the discriminant of O. This asymptotic complexity outperforms all other available methods for computing isogenies.We also show that a variant of our method has asymptotic run time e exp(Õ(√log(|Δ|))) while requesting only polynomial memory (both quantum and classical). 
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