TY - GEN
T1 - Isogeny volcanoes and the SEA algorithm
AU - Fouquet, Mireille
AU - Morain, François
N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2002.
PY - 2002/1/1
Y1 - 2002/1/1
N2 - Recently, Kohel gave algorithms to compute the conductor of the endomorphism ring of an ordinary elliptic curve, given the cardinality of the curve. Using his work, we give a complete description of the structure of curves related via rational l-degree isogenies, a structure we call a volcano. We explain how we can travel through this structure using modular polynomials. The computation of the structure is possible without knowing the cardinality of the curve, and that as a result, we deduce information on the cardinality.
AB - Recently, Kohel gave algorithms to compute the conductor of the endomorphism ring of an ordinary elliptic curve, given the cardinality of the curve. Using his work, we give a complete description of the structure of curves related via rational l-degree isogenies, a structure we call a volcano. We explain how we can travel through this structure using modular polynomials. The computation of the structure is possible without knowing the cardinality of the curve, and that as a result, we deduce information on the cardinality.
UR - https://www.scopus.com/pages/publications/84958550268
U2 - 10.1007/3-540-45455-1_23
DO - 10.1007/3-540-45455-1_23
M3 - Conference contribution
AN - SCOPUS:84958550268
SN - 3540438637
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 276
EP - 291
BT - Algorithmic Number Theory - 5th International Symposium, ANTS-V Sydney, Australia, July 7-12, 2002 Proceedings
A2 - Fieker, Claus
A2 - Kohel, David R.
PB - Springer Verlag
T2 - 5th International Algorithmic Number Theory Symposium, ANTS 2002
Y2 - 7 July 2002 through 12 July 2002
ER -