@article{MVK_2020_11_2_a5,
author = {E. S. Malygina and S. A. Novoselov},
title = {Division polynomials for hyperelliptic curves defined by {Dickson} polynomials},
journal = {Matemati\v{c}eskie voprosy kriptografii},
pages = {69--81},
year = {2020},
volume = {11},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/MVK_2020_11_2_a5/}
}
TY - JOUR AU - E. S. Malygina AU - S. A. Novoselov TI - Division polynomials for hyperelliptic curves defined by Dickson polynomials JO - Matematičeskie voprosy kriptografii PY - 2020 SP - 69 EP - 81 VL - 11 IS - 2 UR - http://geodesic.mathdoc.fr/item/MVK_2020_11_2_a5/ LA - en ID - MVK_2020_11_2_a5 ER -
E. S. Malygina; S. A. Novoselov. Division polynomials for hyperelliptic curves defined by Dickson polynomials. Matematičeskie voprosy kriptografii, Tome 11 (2020) no. 2, pp. 69-81. http://geodesic.mathdoc.fr/item/MVK_2020_11_2_a5/
[1] Tate J., “Endomorphisms of Abelian varieties over finite fields”, Invent. math., 2:2 (1966), 134—144 | DOI | MR | Zbl
[2] Koblitz N., “Hyperelliptic cryptosystems”, J. Cryptology, 1:3 (1989), 139—150 | DOI | MR | Zbl
[3] Pila J., “Frobenius maps of Abelian varieties and finding roots of unity in finite fields”, Math. Comput., 55:192 (1990), 745—763 | DOI | MR | Zbl
[4] Cantor D. G., “On the analogue of the division polynomials for hyperelliptic curves”, J. reine und angew. Math., 447 (1994), 91—146 | MR
[5] Lidl R., Mullen G. L., Turnwald G., Dickson polynomials, Longman Sci. Tech., Harlow, Essex, England, 1993, 207 pp. | MR | Zbl
[6] Gaudry P., Schost É., “Modular equations for hyperelliptic curves”, Math. Comput., 74:249 (2005), 429—454 | DOI | MR | Zbl
[7] Gaudry P., Thomé E., Thériault N., Diem C., “A double large prime variation for small genus hyperelliptic index calculus”, Math. Comput., 76:257 (2007), 475—492 | DOI | MR | Zbl
[8] Novoselov S.A., Counting points on hyperelliptic curves of type $y^2 = x^{2g+1} + a x^{g+1} + b x$, 2019, arXiv: 1902.05992 | MR | Zbl
[9] Cantor D. G., “Computing in the Jacobian of a hyperelliptic curve”, Math. Comput., 48:177 (1987), 95—101 | DOI | MR | Zbl
[10] Flynn E.V., Yan Bo Ti, Genus two isogeny cryptography, Cryptology ePrint Archive, Report 2019/177 \year 2019 https://eprint.iacr.org/2019/177 | MR
[11] Cohen H., Frei G. et al., Handbook of Elliptic and Hyperelliptic Curve Cryptography, Chapman Hall/CRC, 2005, 848 pp.