Isogeny volcanoes and the SEA algorithm

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2369, Issue , 2002, Pages 276-291

  Fouquet, Mireille ^a   Morain, François ^a  

^a ÉCOLE POLYTECHNIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; NUMBER THEORY; POLYNOMIALS; VOLCANOES;

CARDINALITIES; ELLIPTIC CURVE; ENDOMORPHISM RING; MODULAR POLYNOMIAL;

ALGORITHMS;

EID: 84958550268     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45455-1_23     Document Type: Conference Paper

References (13)

1. Z. I. Borevitch and I. R. Chafarevitch. Théorie des nombres. Gauthiers-Villars, Paris, 1967.
2. J. Chao, O. Nakamura, K. Sobataka, and S. Tsujii. Construction of secure elliptic cryptosystems using CM tests and liftings. In K. Ohta and D. Pei, editors, Advances in Cryptology – ASIACRYPT’98, volume 1514 of Lecture Notes in Comput. Sci., pages 95–109. Springer-Verlag, 1998. Beijing, China.
3. J.-M. Couveignes, L. Dewaghe, and F. Morain. Isogeny cycles and the Schoof-Elkies-Atkin algorithm. Research Report LIX/RR/96/03, LIX, April 1996. Available at http://www.lix.polytechnique.fr/Labo/Francois.Morain/.
4. J.-M. Couveignes and F. Morain. Schoof’s algorithm and isogeny cycles. In ANTSI, 1994.
5. D. H. Cox. Primes of the Form x2 + ny2. Wiley-Interscience, 1989.
6. M. Deuring. Die Typen der Multiplikatorenringe elliptischer Funktionenkörper. Abh. Math. Sem. Hamburg, 14:197–272, 1941.
7. M. Fouquet. Anneau d’endomorphismes et cardinalité des courbes elliptiques: aspects algorithmiques. Thèse, école polytechnique, December 2001. Available at http://www.lix.polytechnique.fr/Labo/Mireille.Fouquet/.
8. M. Fouquet, P. Gaudry, and R. Harley. An extension of Satoh’s algorithm and its implementation. J. Ramanujan Math. Soc., December 2000.
9. S.D. Galbraith, F. Hess, and N.P. Smart. Extending the GHS weil descent attack. http://eprint.iacr.org/, 2001.
10. D. Kohel. Endomorphism rings of elliptic curves over finite fields. Phd thesis, University of California, Berkeley, 1996.
11. R. Lercier. Algorithmique des courbes elliptiques dans les corps finis. Thèse, école polytechnique, June 1997.
12. T. Satoh. The canonical lift of an ordinary elliptic curve over a finite field and its point counting. J. Ramanujan Math. Soc., 15:247–270, December 2000.
13. R. Schoof. Counting points on elliptic curves over finite fields. J. Théor. Nombres Bordeaux, 1995.