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Comparison of scalar multiplication on real hyperelliptic curves
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Trisection for supersingular genus $2$ curves in characteristic $2$
1. | Departament de Matemàtica, Universitat de Lleida, Jaume II 69, Lleida 25001, Spain |
2. | Departamento de Matemática, Universidad del Bío-Bío, Avenida Collao 1202, Concepción, Chile |
References:
[1] |
D. Cantor, Computing in the Jacobian of a Hyperelliptic curve, Math. Comp., 48 (1987), 95-101.
doi: 10.1090/S0025-5718-1987-0866101-0. |
[2] |
I. Kitamura, M. Katagi and T. Takagi, A complete divisor class halving algorithm for hyperelliptic curve cryptosystems of genus two, in Information Security and Privacy, Springer, 2005, 146-157.
doi: 10.1007/11506157_13. |
[3] |
J. Miret, J. Pujolàs and A. Rio, Explicit 2-power torsion of genus $2$ curves over finite fields, Adv. Math. Commun., 4 (2010), 155-165.
doi: 10.3934/amc.2010.4.155. |
[4] |
F. Oort, Subvarieties of moduli spaces, Invent. Math., 24 (1974), 95-119.
doi: 10.1007/BF01404301. |
[5] |
R. Schoof, Nonsingular plane cubic curves over finite fields, J. Combin. Theory Ser. A, 46 (1987), 183-211.
doi: 10.1016/0097-3165(87)90003-3. |
[6] |
C. Xing, On supersingular abelian varieties of dimension two over finite fields, Finite Fields Appl., 2 (1996), 407-421.
doi: 10.1006/ffta.1996.0024. |
show all references
References:
[1] |
D. Cantor, Computing in the Jacobian of a Hyperelliptic curve, Math. Comp., 48 (1987), 95-101.
doi: 10.1090/S0025-5718-1987-0866101-0. |
[2] |
I. Kitamura, M. Katagi and T. Takagi, A complete divisor class halving algorithm for hyperelliptic curve cryptosystems of genus two, in Information Security and Privacy, Springer, 2005, 146-157.
doi: 10.1007/11506157_13. |
[3] |
J. Miret, J. Pujolàs and A. Rio, Explicit 2-power torsion of genus $2$ curves over finite fields, Adv. Math. Commun., 4 (2010), 155-165.
doi: 10.3934/amc.2010.4.155. |
[4] |
F. Oort, Subvarieties of moduli spaces, Invent. Math., 24 (1974), 95-119.
doi: 10.1007/BF01404301. |
[5] |
R. Schoof, Nonsingular plane cubic curves over finite fields, J. Combin. Theory Ser. A, 46 (1987), 183-211.
doi: 10.1016/0097-3165(87)90003-3. |
[6] |
C. Xing, On supersingular abelian varieties of dimension two over finite fields, Finite Fields Appl., 2 (1996), 407-421.
doi: 10.1006/ffta.1996.0024. |
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