References
N. El Mrabet and M. Joye, Guide to Pairing-Based Cryptography, in Cryptography and Network Security Series (Chapman and Hall/CRC, New York, 2016).
D. Koshelev, Hashing to Elliptic Curves of \(j\)-Invariant \(1728\) , in IACR Cryptology, https:// eprint. iacr.org/2019/1294 (2019).
H. Inose, in Proceedings of the International Symposium on Algebraic Geometry (Books Kinokuniya, Kyoto, 1977), pp. 495–502.
M. Kuwata, Rikkyo Daigaku Sugaku Zasshi 49 (1), 91 (2000).
R. Kloosterman, Commentarii Mathematici Universitatis Sancti Pauli 54 (1), 69 (2005).
A. Kumar and M. Kuwata, Nagoya Mathematical Journal 228, 124 (2017).
T. Shioda, in Proceedings of the Japan Academy, Series A, Mathematical Sciences 76 (5), 68 (2000).
T. Shioda, Journal of the Mathematical Society of Japan 60 (4), 1083 (2008).
T. Shioda and M. Sch+-tt, in Mordell–Weil Lattices, A Series of Modern Surveys in Mathematics (Springer-Verlag, Singapore, 2019), Vol. 70, pp. 79–114.
T. Shioda and H. Inose, in Complex Analysis and Algebraic Geometry (Cambridge University Press, Cambridge, 1977), pp. 119–136.
M. Kuwata and L. Wang, International Mathematics Research Notices 1993 (4), 113 (1993).
J.-F. Mestre, in Comptes Rendus de l’Académie des Sciences, Series I - Mathematics 314 (12), 919 (1992).
D. Ulmer, in Arithmetic of \(L\)-functions, IAS / Park City Mathematics 18, 211 (2011).
D. Koshelev, Magma Code, github: https://github.com/dishport/Hashing-to-elliptic-curves-of-j-0-and- Mordell-Weil-groups (2020).
J. Chahal, M. Meijer, and J. Top, Commentarii Mathematici Universitatis Sancti 49 (1), 79 (1999).
K. Oguiso and T. Shioda, Rikkyo Daigaku Sugaku Zasshi 40 (1), 83 (1991).
I. Shimada and D. Zhang, Nagoya Mathematical Journal 161, 23 (2001).
T. Shioda, Rikkyo Daigaku Sugaku Zasshi 39 (2), 211 (1990).
K. Nishiyama, Japanese Journal of Mathematics 22 (2), 293 (1996).
S. Ma, in Proceedings of the American Mathematical Society 141 (1), 131 (2013).
Acknowledgments
The author expresses his deep gratitude to his scientific advisor M. Tsfasman and thanks A. Trepalin for help and useful comments.
Funding
This work was supported in part by the Russian Foundation for Basic Research under grant no. 19-31-90029\(\backslash\)19.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Koshelev, D. Hashing to Elliptic Curves of \(j=0\) and Mordell–Weil Groups. Math Notes 108, 748–751 (2020). https://doi.org/10.1134/S0001434620110140
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0001434620110140