[Retracted] Image Encryption Algorithm Based on Artificial Bee Colony Algorithm and Chaotic System

Algorithm 1

Bit-plane decomposition and scrambling algorithm based on the fractional-order hyper Lorenz chaotic system.

	Require: Plain image ,
	Ensure: Scrambled image
(1)	/Calculate the hash value of the plaintext image/
(2)
(3)	/Calculate the initial value of the fractional chaotic system/
(4)	Calculate the initial value of the chaotic sequence according to equation (7) to equation (9)
(5)	/Calculate fractional chaotic sequence/
(6)	Calculate chaotic sequence by using , and the given chaotic parameters into equation (1) to calculate, Pre-iterative chaotic mapping 1000 times to eliminate the adverse consequences caused by transient reactions, continue to iterate times
(7)
(8)	Decompose into bit planes to get 8 bit planes
(9)	fordo
(10)	Arrange the bit plane into a one-dimensional vector in column first
(11)	Arrange the chaotic sequence in in ascending order, and generate a sequence used to record the position of each element in the sorted sequence in the original sequence
(12)	Re-arrange the vector in the order of the sequence to obtain a new one-dimensional vector after transformation
(13)	Adjust the size of the newly generated to make it consistent with the size of the plaintext image
(14)	end for
(15)	Combine the obtained 8 scrambled bit-plane images to gain the final scrambled image