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arxiv: 1202.4285 · v2 · pith:5QNVAMFKnew · submitted 2012-02-20 · 🧮 math.NT · cs.CR

Finding ECM-friendly curves through a study of Galois properties

Razvan Barbulescu (INRIA Nancy - Grand Est / LORIA) , Joppe W. Bos (LACAL) , Cyril Bouvier (INRIA Nancy - Grand Est / LORIA) , Thorsten Kleinjung (LACAL) , Peter L. Montgomery This is my paper
classification 🧮 math.NT cs.CR
keywords curvesellipticpropertiesgoodproofsbehaviorcardinalitycertain
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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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