Construction of Secure Elliptic Cryptosystems Using CM Tests and Liftings
ASIACRYPT '98 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Schoof's algorithm and isogeny cycles
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
Isogeny cordillera algorithm to obtain cryptographically good elliptic curves
ACSW '07 Proceedings of the fifth Australasian symposium on ACSW frontiers - Volume 68
Bits Security of the Elliptic Curve Diffie---Hellman Secret Keys
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
On Avoiding ZVP-Attacks Using Isogeny Volcanoes
Information Security Applications
Computing Hilbert class polynomials
ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory
Parallel calculation of volcanoes for cryptographic uses
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
Do all elliptic curves of the same order have the same difficulty of discrete log?
ASIACRYPT'05 Proceedings of the 11th international conference on Theory and Application of Cryptology and Information Security
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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.