Finding ECM-Friendly Curves through a Study of Galois Properties

Details Finding ECM-Friendly Curves through a Study of Galois Properties Finding ECM-Friendly Curves through a Study of Galois Properties

2012-02-20

arxiv.org/abs/1202.4285v1

Mathematics

Number Theory

Algorithmic Number Theory Symposium (2012)

Scientific paper

In this paper we prove some divisibility properties of the cardinal- ity of elliptic curves modulo primes. These proofs explain the good behavior of certain parameters when using Montgomery or Edwards curves in the set- ting 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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