Confidential information exchange electronically in a secure way becomes very important in the age of computers. A newly proposed public key crypto method based on Chebyshev polynomials [16] recommend a new approach to data encryption. This paper provides an overview of three major types of public key cryptosystems mainly Diffie-Hellman Key Exchange Algorithm, the RSA Cryptosystem, the ElGamal Encryption Method and their implementation using Chebyshev Polynomials. During the past decade, there has been tremendous interest world-wide image encryption which is based on edge detail. In this method the image divided into two, one is the image contains edges and another is the image without edges, and encrypt the both images using encryption algorithm. The encrypted images are complex for intruder to decode, so it provides a high level of security.