Abstract
In this paper, we describe a quantum algorithm for computing an isogeny between any two supersingular elliptic curves defined over a given finite field. The complexity of our method is in \(\tilde{O}(p^{1/4})\) where \(p\) is the characteristic of the base field. Our method is an asymptotic improvement over the previous fastest known method which had complexity \(\tilde{O}(p^{1/2})\) (on both classical and quantum computers). We also discuss the cryptographic relevance of our algorithm.
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Biasse, JF., Jao, D., Sankar, A. (2014). A Quantum Algorithm for Computing Isogenies between Supersingular Elliptic Curves. In: Meier, W., Mukhopadhyay, D. (eds) Progress in Cryptology -- INDOCRYPT 2014. INDOCRYPT 2014. Lecture Notes in Computer Science(), vol 8885. Springer, Cham. https://doi.org/10.1007/978-3-319-13039-2_25
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DOI: https://doi.org/10.1007/978-3-319-13039-2_25
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