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)
“No method nor discipline can supersede the necessity of being forever on the alert. What is a course of history or philosophy, or poetry, no matter how well selected, or the best society, or the most admirable routine of life, compared with the discipline of looking always at what is to be seen? Will you be a reader, a student merely, or a seer? Read your fate, see what is before you, and walk on into futurity.”
—Henry David Thoreau (1817–1862)