Finding Suitable Curves for the Elliptic Curve Method of Factorization

DOI10.2307/2153176zbMath0815.11063OpenAlexW4248011490MaRDI QIDQ4293979

François Morain, A. O. L. Atkin

Publication date: 30 June 1994

Full work available at URL: https://doi.org/10.2307/2153176

zbMATH Keywords

factorizationselliptic curve methodcurves with complex multiplication

Mathematics Subject Classification ID

Elliptic curves (14H52) Factorization (11Y05)

Related Items (14)

Constructing Isogenies between Elliptic Curves Over Finite Fields ⋮ A classification of ECM-friendly families of elliptic curves using modular curves ⋮ Improved complexity bounds for counting points on hyperelliptic curves ⋮ High-rank elliptic curves with given torsion group and some applications ⋮ Constructing elliptic curves over finite fields with prescribed torsion ⋮ Elliptic Curves and Primality Proving ⋮ ECM using Edwards curves ⋮ Diophantine triples and construction of high-rank elliptic curves over \(\mathbb{Q}\) with three nontrivial 2-torsion points ⋮ Classifications of Elliptic Fibrations of a Singular K3 Surface ⋮ Computing Hilbert class polynomials with the Chinese remainder theorem ⋮ ECM on Graphics Cards ⋮ Proving primality in essentially quartic random time ⋮ Modular curves over number fields and ECM ⋮ An example of elliptic curve over \(\mathbb{Q}\) with rank equal to 15.

Uses Software

• ECPP

Cites Work

• Unnamed Item
• Factoring integers with elliptic curves
• Elliptic Curves and Primality Proving
• Explicit determination of nontrivial torsion structures of elliptic curves over quadratic number fields
• Speeding the Pollard and Elliptic Curve Methods of Factorization
• A p + 1 Method of Factoring
• Universal Bounds on the Torsion of Elliptic Curves
• Factorizations of 𝑏ⁿ±1, 𝑏=2, 3, 5, 6, 7, 10, 11, 12 Up to High Powers

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