CRYPTOGRAPHY WITH ELLIPTIC CURVES
Tarun Narayan Shankar, G. Sahoo · 2009
paper describes the basic idea of Elliptic Curve Cryptography(ECC) and its implementation through co-ordinate geometry for data encryption. Elliptic curve cryptography is an asymmetric key cryptography. It includes (i) public key generation on the elliptic curve and its declaration for data encryption and (ii) private key generation and its use in data decryption depended on the points on two dimensional elliptical curve. We also discuss the implementation of ECC on two finite fields, prime field and binary field. An overview of ECC implementation on two dimensional representation of plaintext coordinate systems and data encryption through Elgamal Encryption technique has been discussed. Much attention has been given here on the mathematics of elliptic curves starting with their derivations and the proof of how points upon them form an additive abelian group for cryptographic purposes, specifically results for the group formed by an elliptic curve over a finite field, E(Fp),E(F 2 m ), and showing how this can form public key cryptographic systems for use in both encryption and key exchange. Finally, we describe how to encrypt the data with the alphabetical table.