Hyperelliptic Curve Method (HECM)
There are recent developments in using hyperelliptic curves to factor integers. Cosset shows in his article (of 2010) that one can build a hyperelliptic curve with genus two (so a curve with of degree 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.
Read more about this topic: Lenstra Elliptic Curve Factorization
Famous quotes containing the words curve and/or method:
“In philosophical inquiry, the human spirit, imitating the movement of the stars, must follow a curve which brings it back to its point of departure. To conclude is to close a circle.”
—Charles Baudelaire (1821–1867)
““English! they are barbarians; they don’t believe in the great God.” I told him, “Excuse me, Sir. We do believe in God, and in Jesus Christ too.” “Um,” says he, “and in the Pope?” “No.” “And why?” This was a puzzling question in these circumstances.... I thought I would try a method of my own, and very gravely replied, “Because we are too far off.” A very new argument against the universal infallibility of the Pope.”
—James Boswell (1740–1795)