Key Generation in Elliptic Curve Cryptosystems over GF ( 2 n )

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 are used with 3BC (Block Byte Bit Cipher) algorithm for the data encryption. We are investigating a novel approach of software/ hardware co-design implemented in Verilog Hardware Description Language (VHDL), which produces hardware algorithm components to place onto the FPGAs, thereby creating adaptive software overlays differentiated by use of a Universal Unique Identifier (UUID) as a functional operand to a custom arithmetic Logic Unit (ALU).1