A New Digital Signature Scheme Based on Mandelbrot and Julia Fractal Sets

Abstract

This paper describes a new cryptographic digital signature scheme based on Mandelbrot and Julia fractal sets. Having fractal based digital signature scheme is possible due to the strong connection between the Mandelbrot and Julia fractal sets. The link between the two fractal sets used for the conversion of the private key to the public key. Mandelbrot fractal function takes the chosen private key as the input parameter and generates the corresponding public-key. Julia fractal function then used to sign the message with receiver's public key and verify the received message based on the receiver's private key. The propose scheme was resistant against attacks, utilizes small key size and performs comparatively faster than the existing DSA, RSA digital signature scheme. Fractal digital signature scheme was an attractive alternative to the traditional number theory digital signature scheme.