Fast projective synchronization of fractional order chaotic and reverse chaotic systems with its application to an affine cipher using date of birth (DOB)

In this paper, a fractional order dynamical system is constructed that exhibits chaotic and reverse chaotic attractors by changing the sign of the one parameter which involves in the existence of the phase reversal function. A new method of fast projective synchronization of fractional order dynamical systems is introduced. An affine cipher is proposed for secure communication based on the solutions of the synchronized fractional order chaotic systems with the support of the sender's and receiver's date of birth. The efficiency and security of an affine cipher are analyzed. Numerical simulations are demonstrated to show the feasibility of the presented theory.