But the NSA (and many security researchers) have also been touting new codes based on a different sort of mathematics involving elliptic curves.
He has no proof, he stresses, but "I think it's a good guess that the NSA knows something about elliptic curves that we don't.
Pseudowintera colorata, of New Zealand, has peppery, elliptic, red-blotched leaves on a 10-metre (32-foot) tree.
Meanwhile, Gerhard Frey of Germany had pointed out that, if Fermat's last theorem is false, so that there are integers u, v, w such that up + vp = wp (p greater than 5), then for these values of u, v, and p the curve y2 = x(x − up)(x + vp) has properties that contradict major conjectures of the Japanese mathematicians Taniyama Yutaka and Shimura Goro about elliptic curves.
More significantly still, in the 1960s Atiyah, the American Isadore Singer, and others found ways of connecting this work to the study of a wide variety of questions involving partial differentiation, culminating in the celebrated Atiyah-Singer theorem for elliptic operators.
The leaves, 5 12.5 cm (2 5 inches) long, are glossy and light green in colour and ovate to elliptic in outline; the flowers are small and inconspicuous.
The elliptic leaves have coarsely serrate (toothed) margins and are 200 250 mm (8 10 inches) in length.
Charles Hermite, (born Dec. 24, 1822, Dieuze, Fr. died Jan . 14 , 1901Paris) French mathematician whose work in the theory of functions includes the application of elliptic functions to provide the first solution to the general equation of the fifth degree, the quintic equation.
Earlier in the month a group of Brazilian mathematicians released a set of new codes for a scrambling system called elliptic-curve cryptography, for use by those worried that officially-recommended ones might be tainted.
And a group of Brazilian mathematicians has published a new set of codes for use with elliptic-curve cryptography, a novel scrambling technique that has been championed by the NSA.
Winter's bark has leathery, elliptic-shaped leaves; red-tinged shoots; and jasmine-scented, cream-coloured, 8- to 12-petaled, 2.5-centimetre (1-inch) flowers in clusters.
