Editing Lenstra elliptic-curve factorization (section)

==Hyperelliptic-curve method (HECM)==

There are recent developments in using [[hyperelliptic curve]]s to factor integers. Cosset shows in his article (of 2010) that one can build a hyperelliptic curve with genus two (so a curve <math>y^2 = f(x)</math> with {{mvar|f}} of degree&nbsp;5), which gives the same result as using two "normal" elliptic curves at the same time. By making use of the Kummer surface, calculation is more efficient. The disadvantages of the hyperelliptic curve (versus an elliptic curve) are compensated by this alternative way of calculating. Therefore, Cosset roughly claims that using hyperelliptic curves for factorization is no worse than using elliptic curves.