Finding ECM-Friendly Curves through a Study of Galois Properties
نویسندگان
چکیده
In this paper we prove some divisibility properties of the cardinality of elliptic curves modulo primes. These proofs explain the good behavior of certain parameters when using Montgomery or Edwards curves in the setting of the elliptic curve method (ECM) for integer factorization. The ideas of the proofs help us to find new families of elliptic curves with good division properties which increase the success probability of ECM.
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عنوان ژورنال:
- IACR Cryptology ePrint Archive
دوره 2012 شماره
صفحات -
تاریخ انتشار 2012