Constructing elliptic curve isogenies in quantum subexponential time

• Published in: Journal of mathematical cryptology Vol. 8; no. 1; pp. 1 - 29
• Main Authors: Childs, Andrew, Jao, David, Soukharev, Vladimir
• Format: Journal Article
• Language: English
• Published: Berlin Walter de Gruyter GmbH 01.02.2014; De Gruyter
• Subjects: 11Y40; 14H52; 68Q12; 81P94; Algorithms; Cryptography; Elliptic curves; hidden shift problem; isogenies; quantum algorithms

Given two ordinary elliptic curves over a finite field having the same cardinality and endomorphism ring, it is known that the curves admit a nonzero isogeny between them, but finding such an isogeny is believed to be computationally difficult. The fastest known classical algorithm takes exponential...