Elliptic curve cryptosystems (ECC) are new generations of public key cryptosystems that have a smaller key size for the same level of security. The exponentiation on elliptic curve is the most important operation in ECC, so when the ECC is put into practice, the major problem is how to enhance the speed of the exponentiation. It is thus of great interest to develop algorithms for exponentiation...

‎In this paper‎, ‎we propose some Diffie-Hellman type key exchange protocols using isogenies of elliptic curves‎. ‎The first method which uses the endomorphism ring of an ordinary elliptic curve $ E $‎, ‎is a straightforward generalization of elliptic curve Diffie-Hellman key exchange‎. ‎The method uses commutativity of the endomorphism ring $ End(E) $‎. ‎Then using dual isogenies‎, ‎we propose...

As part of their great burst of activity in the late 1970s, Cheng and Yau proved many geometric results concerning differential structures invariant under affine transformations of R n. Affine differential geometry is the study of those differential properties of hypersurfaces in R n+1 which are invariant under volume-preserving affine transformations. One way to develop this theory is to start...

Two new species of Dilkea subgenus Dilkea (Passifloraceae) are described from Loreto, Peru. Dilkea hebes Feuillet, sp. nov., has leaves with elliptic to oblanceolate blades that are dull adaxially, and spherical fruits with thick walls; Dilkea nitens Feuillet, sp. nov., has leaves with narrow-ovate blades that are shiny adaxially, and fruits with an apical cone and thin walls. A key to the spec...

In this paper, we describe the spaces of stability conditions for the triangulated categories associated to three dimensional Calabi-Yau fibrations. We deal with two cases, the flat elliptic fibrations and smooth K3 (Abelian) fibrations. In the first case, we will see there exist chamber structures similar to those of the movable cone used in birational geometry. In the second case, we will com...

We derive an analytical form for jet-correlation flow-background in a cluster approach. We argue that the elliptic flow parameter to be used in jetcorrelation background is that from two-particle method excluding non-flow correlation irrelevant to reaction plane, but including cross-terms between cluster correlation and cluster flow. We verify our result with Monte Carlo simulations. We discuss...

X iv :m at h/ 02 10 08 4v 1 [ m at h. C A ] 7 O ct 2 00 2 Abstract. Recently Wolff [28] obtained a sharp L2 bilinear restriction theorem for bounded subsets of the cone in general dimension. Here we adapt the argument of Wolff to also handle subsets of “elliptic surfaces” such as paraboloids. Except for an endpoint, this answers a conjecture of Machedon and Klainerman, and also improves upon th...