Abstract: In this study, we are proposing a new cryptographic public-key encryption protocol based on Mandelbrot and Julia fractal sets. The fractal based public-key encryption protocol is possible because of the strong connection between the Mandelbrot and Julia fractal sets. In the proposed protocol, Mandelbrot fractal function takes the chosen private key as the input parameter and generates the corresponding public-key. Julia fractal function is used to cipher the plaintext with receiver`s public key and decipher the ciphertext based on the receiver`s private key. The proposed protocol is designed to be resistant against attacks, utilize small key size and perform comparatively faster than the existing RSA public-key encryption protocol. The proposed fractal public-key encryption protocol is, therefore, an attractive alternative to the traditional number theory based public-key encryption protocol.