Cryptanalysis and Improvement of Chaos-Based Image Encryption Scheme with Circular Inter-Intra-Pixels Bit-Level Permutation

Table 4

Correlation coefficients in different directions by different algorithms.

Image	Direction	Plain image	Algorithm
			Ref. [21]	Ref. [22]	Ref. [23]	Original	Improved
Lena	Horizontal	0.9456	−0.0086	−0.0066	0.0011	0.0098	0.0057
	Vertical	0.9727	−0.0102	−0.0089	0.0098	−0.0013	−0.0001
	Diagonal	0.9213	−0.0125	0.0424	−0.0227	−0.0009	0.0031
Peppers	Horizontal	0.9664	−0.0089	0.0194	0.0071	0.0099	−0.0017
	Vertical	0.9738	−0.0113	−0.0091	−0.0065	−0.0016	−0.0033
	Diagonal	0.9423	0.0045	0.0123	−0.0165	−0.0012	0.0035
Couple	Horizontal	0.9299	−0.0178	−0.0122	−0.0236	0.0145	−0.0056
	Vertical	0.8878	−0.0025	0.0262	−0.0045	0.0035	−0.0017
	Diagonal	0.8382	0.0001	−0.0257	0.0016	0.0046	−0.0085
Cameraman	Horizontal	0.9335	−0.0211	0.0063	−0.0047	0.0138	0.0030
	Vertical	0.9592	−0.0103	−0.0142	−0.0195	0.0031	−0.0020
	Diagonal	0.9087	0.0054	0.0168	0.0279	−0.0010	0.0009
Boat	Horizontal	0.9494	−0.0054	−0.0189	−0.0295	0.0078	0.0028
	Vertical	0.9553	−0.0009	0.0003	−0.0150	0.0027	0.0008
	Diagonal	0.9118	0.0026	−0.0204	−0.0224	0.0050	0.0035