Table 16 Performance comparisons analysis.

Reference	Image	Horizontal correlation coefficient	Vertical correlation coefficient	Diagonal correlation coefficient	NPCR	UACI	Entropy	Key space
REF ²⁴	Lena	− 0.0021	0.0051	0.0068	99.62	33.48	7.9990	10⁶² ≈ 2²⁰⁷
REF ¹⁷	Lena	− 0.0067	− 0.0176	− 0.0151	99.59	33.49	7.9970	10⁴² ≈ 2¹⁴⁰
REF ¹⁹	Lena	− 0.0044	0.0096	− 0.0021	99.61	33.46	7.9992	10 ⁷⁷≈ 2²⁵⁶
REF ⁴²	Lena	− 0.0032	− 0.0012	− 0.0024	99.63	32.92	7.9970	10⁸⁰ ≈ 2²⁶⁵
REF ⁴³	Lena	− 0.0001	− 0.0003	− 0.0004	99.60	33.40	7.9817	10³⁰ ≈ 2⁴⁴⁹
REF ⁴⁴	Lena	0.0001	0.0012	− 0.0030	99.61	–	7.9976	10¹⁰⁵ ≈ 2³⁴⁸
REF ⁴⁵	Lena	0.0073	0.0115	− 0.0012	99.60	33.46	7.9897	10¹¹¹ ≈ 2³⁶⁹
Proposed algorithm	Airplane_0001	− 0.0021	− 0.0029	− 0.0045	99.97	33.61	7.9974	10²⁰² ≈ 2⁶⁷⁴
Proposed algorithm	Lena	− 0.0003	− 0.0025	− 0.0012	99.94	33.35	7.9965	10²⁰² ≈ 2⁶⁷⁴

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