This paper proposes a public key generation for an ECC (Elliptic Curve Cryptosystem) using FPGA’s. To improve the strength of encryption and the speed of processing, the public key and the private key of EC(Elliptic curve) over GF(2) are used to form a shared private key (X,Y). And then the X is used with an initial point on HEC(Hyper-Elliptic Curve) over GF(2) to generate session keys, which a...

1. Introduction. If we wish to write the equations of curves of genus 1 that give elements of the Shafarevich-Tate group of an elliptic curve over a number field K, a choice of ways is open to us. For example, if the element in question is of order 3 the curve of genus 1 corresponding to it occurs as a smooth plane cubic curve over K. In a recent article [C-M] we raised the question of when one...

The modular curve X1(N) parametrizes elliptic curves with a point of order N . For N ≤ 50 we obtain plane models of X1(N) that have been optimized for fast computation, and provide explicit birational maps to transform a point on our model of X1(N) to an elliptic curve. Over a finite field, these allow us to quickly construct elliptic curves containing a point of order N , and can accelerate th...

this study was conducted to investigate the spatial variability of model parameters of soil shrinkage curve in cherlgerd district, chaharmahal-va-bakhtiari province. ninety nine locations were selected and soil clods were collected from the 0-10 cm layer and brought to the laboratory. soil shrinkage curve was measured, according to archimedes's principle, by covering the undisturbed clods ...