Table 4 Comparison between the proposed dynamic S-box (\(\mathcal {S}_{\mathcal {P}})\) and other existing S-box generators.

S-boxes	Nonlinearity over eight boolean functions	Nonlinearity over 256 boolean functions	LAP	DAP	AC	SAC		BIC-SAC		BU	AI
S-boxes	Nonlinearity over eight boolean functions	Nonlinearity over 256 boolean functions	LAP	DAP	AC	Min	Max	Min	Max	BU	AI
Proposed S-box \((\mathcal {S}_{\mathcal {P}})\)	106	94	0.133	0.047	255	0.375	0.594	0.484	0.525	20	104
¹⁶	100	86	0.164	0.039	255	0.421	0.578	0.471	0.527	20	104
¹⁷	98	94	0.133	0.039	251	0.391	0.578	0.476	0.519	18	96
¹⁸	102	92	0.140	0.047	254	0.391	0.594	0.457	0.533	22	88
²⁰	104	92	0.141	0.047	255	0.406	0.593	0.460	0.533	22	104
²¹	102	94	0.133	0.047	254	0.375	0.609	0.478	0.519	20	88
²²	104	94	0.133	0.039	255	0.421	0.625	0.466	0.533	18	96
³⁷	104	84	0.172	0.047	254	0.422	0.578	0.428	0.531	24	104
³⁸	106	92	0.141	0.039	254	0.391	0.625	0.469	0.529	20	104
³⁹	104	94	0.133	0.047	254	0.352	0.586	0.477	0.521	20	96
⁴⁰	106	94	0.133	0.047	254	0.406	0.594	0.469	0.529	18	96
⁴¹	106	94	0.133	0.039	255	0.406	0.609	0.482	0.541	18	96
⁴²	106	94	0.148	0.039	254	0.422	0.594	0.471	0.533	20	104
⁴³	106	90	0.148	0.047	254	0.391	0.609	0.472	0.525	18	96
¹⁰	106	94	0.148	0.047	255	0.437	0.593	0.464	0.544	20	100
⁴⁴	104	92	0.141	0.054	253	0.406	0.594	0.461	0.522	44	120
⁴⁶	106	90	0.148	0.047	255	0.406	0.641	0.471	0.537	20	112
⁴⁷	104	94	0.145	0.039	255	0.391	0.625	0.471	0.531	20	104
¹¹	106	80	0.188	0.039	253	0.406	0.609	0.465	0.527	24	96
⁴⁹	96	90	0.148	0.047	254	0.391	0.625	0.477	0.531	22	104
⁴⁸	100	94	0.152	0.039	255	0.391	0.586	0.468	0.537	22	96
⁵³	106	94	0.152	0.039	255	0.391	0.586	0.468	0.537	18	104
⁵²	106	90	0.152	0.047	255	0.391	0.586	0.468	0.537	24	96

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