1 |
N. Elkies, Elliptic and modular curves over finite fields and related computational issues, Computational perspectives on number theory, AMS/IP Stud. Adv. Math. 7 (1998), Math. Soc., 21-76.
|
2 |
M. Gonda, K. Matsuo, K. Aoki, and J. Chao, Improvements of Addition Algorithm on Genus 3 Hyperelliptic Curves and Their Implementation, IEICE TRANS. FUNDAMENTALS E88-A(1) (2005), 89-96.
DOI
|
3 |
R. H. Hudson and K. S. Williams, Binomial Coefficients and Jacobi Sums, Trans. Amer. Math. Soc. 281 (1984), 431-505.
DOI
ScienceOn
|
4 |
P. Gaudry and R. Harley, Counting points on hyperelliptic curves over finite fields, ANTSIV, W. Bosma ed., LNCS 1838 (2000), Springer-Verlag, 297-312.
|
5 |
I. Blake, G. Seroussi and N. Smart, Elliptic curves in cryptography, London Math. Soc. Lecture Note Series 265 (1999).
|
6 |
H. Yui. On the jacobian varieties of hyperelliptic curves over fields of characteristic , J. Algebra 52 (1987), 378-410.
|
7 |
R. Schoof, Elliptic curves over finite fields and the computation of square roots mod p, Math. Comp. 44 (1985), 483-494.
|
8 |
Yu. I. Manin, The Hasse-Witt matrix of an algebraic curve, AMS Trans. Ser. 2 45 (1965), 245-264.
|
9 |
E. Furukawa, M. Kawazoe, and T.Takahashi, Counting Points for Hyperelliptic Curves of Type = + ax over Finite Prime Fields, LNCS 2004, 26-41.
|
10 |
J. Buhler and N. Koblitz, Lattics Basis Reduction, Jacobi Sums and Hyperelliptic Cryptosystems, Bull. Austral. Math. Soc. 58 (1998), 147-154.
DOI
|
11 |
D. Mumford, Tata Lectures on Theta II, Progress in Mathematics 43, Birkhauser, 1984.
|
12 |
R. Lercier, Algorithmique des courbes elliptiques dans les corps finis. These, Ecole polytechnique, June 1997.
|
13 |
L. Adleman and M. D. Huang, Counting points on curves and abelian varieties over finite fields, J. Symb. Comp. 32(3) (2001) pp. 171-189.
DOI
ScienceOn
|
14 |
M. D. Huang and D. Ierardi, Counting points on curves over finite fields, J. Symb. Comp. 25(1), pp. 1-21 (1998)
DOI
ScienceOn
|
15 |
J. Pila, Frobenius maps of abelian varieites and finding roots of unity in finite fields, Math. Comp. 55(192), pp. 745-763 (1990)
DOI
ScienceOn
|
16 |
K.S. Kedlaya, Counting points on hyperelliptic curves using Monsky-Washnitzer cohomology, J. Ramanujan Math. Soc. 16 (2001), 323-338.
|
17 |
T. Satoh, The canonical lift of an ordinary elliptic curve over a finite field and its point counting, J. Ramanujan Math. Soc. 15 (2000), 247-270.
|
18 |
J. Denef and F. Vercauteren, An Extension of Kedlaya's Algorithm to Hyperelliptic Curves in Characteristic 2, J. Cryptology 19 (2006), 1-25.
DOI
|
19 |
S. Haloui, The characteristic polynomials of abelain varieites of dimensions 3 over finite fields, J. number theory, 2011.
|