The Effect of the Primitive Irreducible Polynomial on the Quality of Cryptographic Properties of Block Ciphers

Table 22

Comparison of the performance indexes of the proposed S-boxes with some standard S-boxes.

S-boxes	Nonlinearity	SAC	BIC	BIC-SAC	DP	LP
AES S-box	112	0.5058	112	0.504	0.0156	0.062
APA S-box	112	0.4987	112	0.499	0.0156	0.062
Gray S-box	112	0.5058	112	0.502	0.0156	0.062
Skipjack S-box	105.7	0.4980	104.1	0.499	0.0468	0.109
Xyi S-box	105	0.5048	103.7	0.503	0.0468	0.156
Residue prime	99.5	0.5012	101.7	0.502	0.2810	0.132
Reference [27]	106	0.4978	103.92	—	—	—
Reference [28]		0.505	—	—	—	—
Reference [29]	104	0.5241	103	0.50181	0.1625	0.0486
S-box 1	112	0.496094	112	0.50119	0.015625	0.0625
S-box 2	112	0.495117	112	0.50600	0.015625	0.0625
S-box 3	112	0.494141	112	0.50202	0.015625	0.0625
S-box 4	112	0.50708	112	0.50656	0.015625	0.0625
S-box 5	112	0.503174	112	0.50105	0.015625	0.0625
S-box 6	112	0.501709	112	0.49819	0.015625	0.0625
S-box 7	112	0.502441	112	0.50593	0.015625	0.0625
S-box 8	112	0.503906	112	0.50251	0.015625	0.0664
S-box 9	112	0.485596	112	0.50258	0.015625	0.0625
S-box 10	112	0.509766	112	0.50739	0.015625	0.0625
S-box 11	112	0.50415	112	0.49784	0.015625	0.0625
S-box 12	112	0.501221	112	0.49679	0.015625	0.0625
S-box 13	112	0.500977	112	0.50021	0.015625	0.0625
S-box 14	112	0.508301	112	0.50718	0.015625	0.0625
S-box 15	112	0.498779	112	0.50265	0.015625	0.0625
S-box 16	112	0.496582	112	0.50544	0.015625	0.0625