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Onuki, Y. Aikawa, T. Yamazaki, and T. Takagi, \u201c(Short paper) a faster constant-time algorithm of csidh keeping two points,\u201d Advances in Information and Computer Security, N. Attrapadung and T. Yagi, eds., pp.23-33, Springer International Publishing, Cham, 2019. 10.1007\/978-3-030-26834-3_2","DOI":"10.1007\/978-3-030-26834-3_2"},{"key":"2","unstructured":"[2] National Institute of Standards and Technology (NIST) \u201cNIST Post-Quantum Cryptography Standardization,\u201d https:\/\/csrc.nist.gov\/Projects\/Post-Quantum-Cryptography"},{"key":"3","unstructured":"[3] D. Jao, R. Azarderakhsh, M. Campagna, C. Costello, L. De Feo, B. Hess, A. Jalali, B. Koziel, B. LaMacchia, P. Longa, M. Naehrig, G. Pereira, J. Renes, V. Soukharev, and D. Urbanik, \u201cSIKE-Supersingular isogeny key encapsulation,\u201d Submission to the NIST Post-Quantum Cryptography Standardization project; https:\/\/sike.org"},{"key":"4","doi-asserted-by":"publisher","unstructured":"[4] D. Jao and L. De Feo, \u201cTowards quantum-resistant cryptosystems from supersingular elliptic curve isogenies,\u201d Post-Quantum Cryptography, B.Y. Yang, ed., pp.19-34, Springer Berlin Heidelberg, Berlin, Heidelberg, 2011. 10.1007\/978-3-642-25405-5_2","DOI":"10.1007\/978-3-642-25405-5_2"},{"key":"5","doi-asserted-by":"crossref","unstructured":"[5] S.D. Galbraith, C. Petit, B. Shani, and Y.B. Ti, \u201cOn the security of supersingular isogeny cryptosystems,\u201d Advances in Cryptology-ASIACRYPT 2016, J.H. Cheon and T. Takagi, eds., pp.63-91, Springer Berlin Heidelberg, Berlin, Heidelberg, 2016. 10.1007\/978-3-662-53887-6_3","DOI":"10.1007\/978-3-662-53887-6_3"},{"key":"6","doi-asserted-by":"crossref","unstructured":"[6] C. Petit, \u201cFaster algorithms for isogeny problems using torsion point images,\u201d Advances in Cryptology-ASIACRYPT 2017, T. Takagi and T. 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Smith, \u201cTowards practical key exchange from ordinary isogeny graphs,\u201d Advances in Cryptology-ASIACRYPT 2018, T. Peyrin and S. Galbraith, eds., pp.365-394, Springer International Publishing, Cham, 2018. 10.1007\/978-3-030-03332-3_14","DOI":"10.1007\/978-3-030-03332-3_14"},{"key":"11","unstructured":"[11] J. De Feo, \u201cMathematics of isogeny based cryptography,\u201d arXiv:1711.04062 [cs.CR], 2017."},{"key":"12","doi-asserted-by":"publisher","unstructured":"[12] S.D. Galbraith and F. Vercauteren, \u201cComputational problems in supersingular elliptic curve isogenies,\u201d Quantum Information Processing, vol.17, no.10, p.265, 2018. 10.1007\/s11128-018-2023-6","DOI":"10.1007\/s11128-018-2023-6"},{"key":"13","doi-asserted-by":"crossref","unstructured":"[13] W. Castryck, T. Lange, C. Martindale, L. Panny, and J. Renes, \u201cCSIDH: An efficient post-quantum commutative group action,\u201d Advances in Cryptology-ASIACRYPT 2018, T. Peyrin and S. 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