Fast and Robust Image Encryption Scheme Based on Quantum Logistic Map and Hyperchaotic System

Algorithm 1

Image encryption method.

	Input: Plain Image P of size , initial conditions and control parameters for hyperchaotic system (3D Chen’s system), and seeds for the chaotic generator.
	Output: Cipher Image C of size
	Step 1: Plain image P is resized to a dimension of pixels and is stored as , and compute the mean M of any of the edges of the plain image P.
	Step 2: Iterate both Chen’s hyperchaotic system (equation (2)) and quantum logistic map (equation (3)) M times according to the computed mean M.
	Step 3: Generate three chaotic sequences by using a hyperchaotic system with given parameters and initial state values as secret keys.
	Step 4: Separate each of the color pixel of the resized image into its three grayscale components of , then apply XOR function between three components of the resized image and three chaotic sequences produced by chen’s hyperchaotic system. The result is considered as diffused R, G, and B components, which are .
	Step 5: Quantum logistic map is initiated and utilized to generate a chaotic keystream sequence , after that split it into R, G, and B components .
	Step 6: Generate Density matrix which is described as Hermitian matrix .
	Step 7: Employ Density matrix on the diffusion components , as well as the output of quantum logistic map using XNOR function to put each of them in a superposition environment.
	Step 8: The three components of the cipher image are generated by XNORing the output of applying density matrix on the diffused components , and quantum logistic map .
	Step 9: Take transpose of the edges of the plain image P in order to increase the randomness within the plain image by shuffling the pixels.
	Step 10: Recombine the cipher image FC with the shuffled edges of the plain image P to obtain the final cipher image C.