Generation of Dynamical S-Boxes for Block Ciphers via Extended Logistic Map

Table 8

Comparison of our S-boxes and others S-boxes used in typical block ciphers.

	Bijection	Nonlinearity			SAC			BIC			I/O XOR	MELP
		Min	Max	Avg	Min	Max	Avg	SAC	Nonlinearity	DD
Gray [31]	128	112	112	112	0.4375	0.5625	0.4998	0.5026	112	112	0.0156	0.0156
AES [32]	128	112	112	112	0.4531	0.5625	0.5049	0.5046	112	112	0.0156	0.0156
Skipjack [33]	123	100	108	105.12	0.3906	0.5938	0.5027	0.5003	104.03	109	0.0469	0.0549
APA [34]	128	112	112	112	0.4375	0.5625	0.5007	0.4997	112	112	0.0156	0.0156
Ref. [3]	128	102	108	105.25	0.4375	0.5781	0.5056	0.5019	103.78	108	0.0391	0.0977
Ref. [4]	128	104	110	106.25	0.4219	0.5938	0.5039	0.5059	103.35	108	0.0391	0.0791
Ref. [6]	128	90	108	103	0.3438	0.6094	0.4851	0.5018	103.78	108	0.0469	0.0665
Ref. [8]	128	98	107	103.25	0.3828	0.5938	0.5059	0.5033	104.21	108	0.0469	0.0665
Ref. [9]	128	96	106	102.50	0.3906	0.6719	0.5178	0.4790	102.64	106	0.2109	0.1077
Ref. [10]	128	106	108	106.75	0.4219	0.6250	0.5034	0.5015	103.78	108	0.0391	0.0706
Ref. [11]	128	104	108	105.75	0.4219	0.5938	0.4976	0.5013	104.50	108	0.0391	0.0625
Ref. [14]	128	106	108	107.25	0.4219	0.6094	0.5034	0.4980	105.28	108	0.0469	0.0706
Ref. [15]	128	106	108	106.75	0.3594	0.5781	0.4917	0.4998	104.14	108	0.0391	0.0706
Ref. [35]	128	112	112	112	0.4219	0.5469	0.5115	0.4982	108.71	112	0.0313	0.0479
Ref. [36]	128	102	108	106	0.4219	0.5938	0.5002	0.5016	104.42	108	0.0391	0.0881
Ref. [37]	128	106	108	106.75	0.4063	0.5938	0.4971	0.5008	102.92	106	0.0391	0.0791
Ref. [38]	129	103	109	104.87	0.3984	0.5703	0.4966	0.5044	102.96	109	0.0391	0.0706
Ref. [39]	128	96	106	103	0.3906	0.6250	0.5039	0.5010	100.35	106	0.5000	0.0881
Ref. [40]	128	110	112	110.50	0.4375	0.5625	0.4937	0.5033	103.85	106	0.0391	0.0625
Ref. [41]	128	106	108	106.75	0.4219	0.6250	0.5034	0.5015	103.78	108	0.0391	0.0706
Ref. [42]	128	106	108	106.75	0.4219	0.5781	0.5010	0.5005	104.07	108	0.0391	0.0706
Proposal 1	128	96	104	101.75	0.3906	0.5781	0.5012	0.5066	103.42	108	0.0391	0.0706
Proposal 2	128	96	108	102.25	0.4219	0.6094	0.5059	0.5050	103.50	108	0.0469	0.0625