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:
“I have been photographing our toilet, that glossy enameled receptacle of extraordinary beauty.... Here was every sensuous curve of the “human figure divine” but minus the imperfections. Never did the Greeks reach a more significant consummation to their culture, and it somehow reminded me, in the glory of its chaste convulsions and in its swelling, sweeping, forward movement of finely progressing contours, of the Victory of Samothrace.”
—Edward Weston (1886–1958)
“A method of child-rearing is not—or should not be—a whim, a fashion or a shibboleth. It should derive from an understanding of the developing child, of his physical and mental equipment at any given stage, and, therefore, his readiness at any given stage to adapt, to learn, to regulate his behavior according to parental expectations.”
—Selma H. Fraiberg (20th century)