APN functions obtained via polynomial expansion in small dimensions
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ID
Representative
Equivalent to
Orthoderivative diff. spec.
8.1
α
170
x
192
+
α
85
x
132
+
x
6
+
x
3
{\displaystyle \alpha ^{170}x^{192}+\alpha ^{85}x^{132}+x^{6}+x^{3}}
SW 19
0
37872
,
2
22788
,
4
4068
,
6
492
,
8
60
{\displaystyle 0^{37872},2^{22788},4^{4068},6^{492},8^{60}}
8.2
x
66
+
α
85
x
33
+
x
18
+
x
9
+
x
3
{\displaystyle x^{66}+\alpha ^{85}x^{33}+x^{18}+x^{9}+x^{3}}
SW 11
0
38040
,
2
22461
,
4
4218
,
6
513
,
8
36
,
10
12
{\displaystyle 0^{38040},2^{22461},4^{4218},6^{513},8^{36},10^{12}}
8.3
x
66
+
α
85
x
33
+
α
17
x
9
+
α
102
x
6
+
x
3
{\displaystyle x^{66}+\alpha ^{85}x^{33}+\alpha ^{17}x^{9}+\alpha ^{102}x^{6}+x^{3}}
SW 13
0
38076
,
2
22311
,
4
4374
,
6
495
,
8
24
{\displaystyle 0^{38076},2^{22311},4^{4374},6^{495},8^{24}}
8.4
α
85
x
132
+
α
85
x
72
+
x
9
+
x
6
+
x
3
{\displaystyle \alpha ^{85}x^{132}+\alpha ^{85}x^{72}+x^{9}+x^{6}+x^{3}}
SW 12
0
38160
,
2
22104
,
4
4536
,
6
456
,
8
24
{\displaystyle 0^{38160},2^{22104},4^{4536},6^{456},8^{24}}
8.5
x
66
+
x
12
+
α
85
x
6
+
x
3
{\displaystyle x^{66}+x^{12}+\alpha ^{85}x^{6}+x^{3}}
SW 6
0
38160
,
2
22164
,
4
4428
,
6
492
,
8
36
{\displaystyle 0^{38160},2^{22164},4^{4428},6^{492},8^{36}}
8.6
x
129
+
α
85
x
24
+
x
12
+
x
9
+
x
3
{\displaystyle x^{129}+\alpha ^{85}x^{24}+x^{12}+x^{9}+x^{3}}
SW 8
0
38184
,
2
22179
,
4
4338
,
6
531
,
8
48
{\displaystyle 0^{38184},2^{22179},4^{4338},6^{531},8^{48}}
8.7
α
170
x
132
+
α
85
x
66
+
α
85
x
18
+
x
3
{\displaystyle \alpha ^{170}x^{132}+\alpha ^{85}x^{66}+\alpha ^{85}x^{18}+x^{3}}
new
0
38196
,
2
22008
,
4
4608
,
6
456
,
8
12
{\displaystyle 0^{38196},2^{22008},4^{4608},6^{456},8^{12}}
8.8
α
85
x
132
+
α
85
x
72
+
x
36
+
x
24
+
x
3
{\displaystyle \alpha ^{85}x^{132}+\alpha ^{85}x^{72}+x^{36}+x^{24}+x^{3}}
SW 9
0
38256
,
2
22116
,
4
4230
,
6
648
,
8
30
{\displaystyle 0^{38256},2^{22116},4^{4230},6^{648},8^{30}}
8.9
α
85
x
192
+
x
72
+
x
33
+
x
24
+
x
9
+
α
153
x
6
{\displaystyle \alpha ^{85}x^{192}+x^{72}+x^{33}+x^{24}+x^{9}+\alpha ^{153}x^{6}}
SW 17
0
38388
,
2
21723
,
4
4626
,
6
507
,
8
36
{\displaystyle 0^{38388},2^{21723},4^{4626},6^{507},8^{36}}
8.10
α
221
x
96
+
α
221
x
33
+
x
12
+
x
9
+
x
6
+
α
187
∗
x
3
{\displaystyle \alpha ^{221}x^{96}+\alpha ^{221}x^{33}+x^{12}+x^{9}+x^{6}+\alpha ^{187}*x^{3}}
SW 10
0
38439
,
2
21618
,
4
4671
,
6
528
,
8
24
{\displaystyle 0^{38439},2^{21618},4^{4671},6^{528},8^{24}}
8.11
α
238
x
144
+
x
132
+
α
51
x
96
+
α
119
x
48
+
x
33
+
x
9
{\displaystyle \alpha ^{238}x^{144}+x^{132}+\alpha ^{51}x^{96}+\alpha ^{119}x^{48}+x^{33}+x^{9}}
SW 16
0
38457
,
2
21552
,
4
4743
,
6
510
,
8
18
{\displaystyle 0^{38457},2^{21552},4^{4743},6^{510},8^{18}}
8.12
α
204
x
160
+
α
51
x
48
+
α
102
x
12
+
α
204
x
10
+
x
9
{\displaystyle \alpha ^{204}x^{160}+\alpha ^{51}x^{48}+\alpha ^{102}x^{12}+\alpha ^{204}x^{10}+x^{9}}
SW 22
0
38844
,
2
20974
,
4
4764
,
6
654
,
8
44
{\displaystyle 0^{38844},2^{20974},4^{4764},6^{654},8^{44}}
8.13
α
160
x
132
+
α
10
x
72
+
x
48
+
α
x
34
+
α
3
x
33
+
α
48
x
18
+
x
17
+
x
3
{\displaystyle \alpha ^{160}x^{132}+\alpha ^{10}x^{72}+x^{48}+\alpha x^{34}+\alpha ^{3}x^{33}+\alpha ^{48}x^{18}+x^{17}+x^{3}}
B 31
0
39150
,
2
20463
,
4
4920
,
6
675
,
8
54
,
10
12
,
12
6
{\displaystyle 0^{39150},2^{20463},4^{4920},6^{675},8^{54},10^{12},12^{6}}
8.14
x
144
+
α
85
x
96
+
α
170
x
80
+
α
85
x
65
+
α
85
x
17
+
x
9
+
x
5
{\displaystyle x^{144}+\alpha ^{85}x^{96}+\alpha ^{170}x^{80}+\alpha ^{85}x^{65}+\alpha ^{85}x^{17}+x^{9}+x^{5}}
B 12668
0
39408
,
2
20072
,
4
4922
,
6
798
,
8
70
,
10
10
{\displaystyle 0^{39408},2^{20072},4^{4922},6^{798},8^{70},10^{10}}
8.15
x
66
+
α
170
x
40
+
x
18
+
α
85
x
5
+
x
3
{\displaystyle x^{66}+\alpha ^{170}x^{40}+x^{18}+\alpha ^{85}x^{5}+x^{3}}
Y 4346
0
39408
,
2
20218
,
4
4692
,
6
838
,
8
104
,
10
12
,
12
8
{\displaystyle 0^{39408},2^{20218},4^{4692},6^{838},8^{104},10^{12},12^{8}}
8.16
x
160
+
x
132
+
x
80
+
x
68
+
x
6
+
x
3
{\displaystyle x^{160}+x^{132}+x^{80}+x^{68}+x^{6}+x^{3}}
SW 20
0
39692
,
2
19752
,
4
4756
,
6
978
,
8
72
,
10
26
,
12
4
{\displaystyle 0^{39692},2^{19752},4^{4756},6^{978},8^{72},10^{26},12^{4}}
ID
Representative
Equivalent to
Orthoderivative diff. spec.
9.1
α
365
x
257
+
x
96
+
x
68
+
α
219
x
33
+
x
5
{\displaystyle \alpha ^{365}x^{257}+x^{96}+x^{68}+\alpha ^{219}x^{33}+x^{5}}
I 4
0
158529
,
2
80829
,
4
18144
,
6
3283
,
8
469
,
10
294
,
12
84
{\displaystyle 0^{158529},2^{80829},4^{18144},6^{3283},8^{469},10^{294},12^{84}}
9.2
α
438
x
129
+
x
66
+
α
219
x
10
+
x
3
{\displaystyle \alpha ^{438}x^{129}+x^{66}+\alpha ^{219}x^{10}+x^{3}}
I 8
0
159418
,
2
79275
,
4
18690
,
6
3213
,
8
742
,
10
252
,
12
21
,
16
21
{\displaystyle 0^{159418},2^{79275},4^{18690},6^{3213},8^{742},10^{252},12^{21},16^{21}}
9.3
x
136
+
x
24
+
x
17
+
α
73
x
10
+
x
3
{\displaystyle x^{136}+x^{24}+x^{17}+\alpha ^{73}x^{10}+x^{3}}
I 3
0
159684
,
2
78687
,
4
19089
,
6
3136
,
8
777
,
10
147
,
12
84
,
14
28
{\displaystyle 0^{159684},2^{78687},4^{19089},6^{3136},8^{777},10^{147},12^{84},14^{28}}
9.4
x
68
+
α
73
x
40
+
x
33
+
x
5
{\displaystyle x^{68}+\alpha ^{73}x^{40}+x^{33}+x^{5}}
I 10
0
159684
,
2
79590
,
4
17871
,
6
3283
,
8
700
,
10
273
,
12
147
,
14
84
{\displaystyle 0^{159684},2^{79590},4^{17871},6^{3283},8^{700},10^{273},12^{147},14^{84}}
9.5
α
73
x
136
+
α
146
x
66
+
α
219
x
10
+
x
3
{\displaystyle \alpha ^{73}x^{136}+\alpha ^{146}x^{66}+\alpha ^{219}x^{10}+x^{3}}
I 16
0
159908
,
2
79086
,
4
18081
,
6
3353
,
8
721
,
10
336
,
12
105
,
14
21
,
16
21
{\displaystyle 0^{159908},2^{79086},4^{18081},6^{3353},8^{721},10^{336},12^{105},14^{21},16^{21}}
9.6
x
264
+
α
73
x
96
+
α
219
x
68
+
x
5
{\displaystyle x^{264}+\alpha ^{73}x^{96}+\alpha ^{219}x^{68}+x^{5}}
I 11
0
160020
,
2
79023
,
4
17997
,
6
3213
,
8
868
,
10
378
,
12
133
{\displaystyle 0^{160020},2^{79023},4^{17997},6^{3213},8^{868},10^{378},12^{133}}
9.7
α
219
x
136
+
x
10
+
x
3
{\displaystyle \alpha ^{219}x^{136}+x^{10}+x^{3}}
I 12
0
160657
,
2
77910
,
4
18312
,
6
3360
,
8
952
,
10
273
,
12
147
,
14
21
{\displaystyle 0^{160657},2^{77910},4^{18312},6^{3360},8^{952},10^{273},12^{147},14^{21}}
9.8
x
192
+
x
66
+
x
17
+
α
73
x
10
+
x
3
{\displaystyle x^{192}+x^{66}+x^{17}+\alpha ^{73}x^{10}+x^{3}}
I 14
0
162183
,
2
76482
,
4
17388
,
6
3871
,
8
1162
,
10
252
,
12
126
,
14
126
,
16
21
,
22
21
{\displaystyle 0^{162183},2^{76482},4^{17388},6^{3871},8^{1162},10^{252},12^{126},14^{126},16^{21},22^{21}}
9.9
α
73
x
192
+
x
136
+
α
365
x
129
+
x
17
+
x
3
{\displaystyle \alpha ^{73}x^{192}+x^{136}+\alpha ^{365}x^{129}+x^{17}+x^{3}}
I 5
0
162708
,
2
77175
,
4
15498
,
6
4270
,
8
1260
,
10
252
,
12
168
,
14
84
,
16
126
,
18
42
,
22
42
,
26
7
{\displaystyle 0^{162708},2^{77175},4^{15498},6^{4270},8^{1260},10^{252},12^{168},14^{84},16^{126},18^{42},22^{42},26^{7}}
9.10
α
73
x
129
+
α
292
x
66
+
x
10
+
x
3
{\displaystyle \alpha ^{73}x^{129}+\alpha ^{292}x^{66}+x^{10}+x^{3}}
I 9
0
163009
,
2
75537
,
4
17283
,
6
4116
,
8
1071
,
10
168
,
12
231
,
14
28
,
16
84
,
18
63
,
20
42
{\displaystyle 0^{163009},2^{75537},4^{17283},6^{4116},8^{1071},10^{168},12^{231},14^{28},16^{84},18^{63},20^{42}}
9.11
x
80
+
α
146
x
66
+
α
73
x
24
+
x
17
{\displaystyle x^{80}+\alpha ^{146}x^{66}+\alpha ^{73}x^{24}+x^{17}}
I 13
0
163366
,
2
75117
,
4
17010
,
6
4536
,
8
966
,
10
252
,
12
63
,
14
154
,
16
63
,
18
84
,
22
21
{\displaystyle 0^{163366},2^{75117},4^{17010},6^{4536},8^{966},10^{252},12^{63},14^{154},16^{63},18^{84},22^{21}}
9.12
x
129
+
α
73
x
66
+
x
17
+
x
10
+
α
365
x
3
{\displaystyle x^{129}+\alpha ^{73}x^{66}+x^{17}+x^{10}+\alpha ^{365}x^{3}}
I 6
0
163996
,
2
74802
,
4
16380
,
6
4368
,
8
1449
,
10
231
,
12
126
,
14
84
,
16
42
,
18
84
,
20
42
,
22
21
,
32
7
{\displaystyle 0^{163996},2^{74802},4^{16380},6^{4368},8^{1449},10^{231},12^{126},14^{84},16^{42},18^{84},20^{42},22^{21},32^{7}}
9.13
α
73
x
136
+
α
219
x
66
+
α
438
x
10
+
x
3
{\displaystyle \alpha ^{73}x^{136}+\alpha ^{219}x^{66}+\alpha ^{438}x^{10}+x^{3}}
I 15
0
168994
,
2
68712
,
4
15141
,
6
6279
,
8
1659
,
10
336
,
12
21
,
14
21
,
16
105
,
18
147
,
20
189
,
24
21
,
26
7
{\displaystyle 0^{168994},2^{68712},4^{15141},6^{6279},8^{1659},10^{336},12^{21},14^{21},16^{105},18^{147},20^{189},24^{21},26^{7}}
9.14
α
438
x
129
+
x
66
+
α
219
x
17
+
x
3
{\displaystyle \alpha ^{438}x^{129}+x^{66}+\alpha ^{219}x^{17}+x^{3}}
I 2
0
169428
,
2
68040
,
4
15561
,
6
6034
,
8
1533
,
10
420
,
12
126
,
14
21
,
16
84
,
18
189
,
20
126
,
22
63
,
26
7
{\displaystyle 0^{169428},2^{68040},4^{15561},6^{6034},8^{1533},10^{420},12^{126},14^{21},16^{84},18^{189},20^{126},22^{63},26^{7}}
9.15
α
365
x
80
+
α
292
x
24
+
α
219
x
17
+
x
3
{\displaystyle \alpha ^{365}x^{80}+\alpha ^{292}x^{24}+\alpha ^{219}x^{17}+x^{3}}
I 17
0
170079
,
2
66297
,
4
16737
,
6
6160
,
8
1407
,
10
420
,
12
21
,
14
42
,
16
63
,
18
210
,
20
133
,
22
63
{\displaystyle 0^{170079},2^{66297},4^{16737},6^{6160},8^{1407},10^{420},12^{21},14^{42},16^{63},18^{210},20^{133},22^{63}}
9.16
x
257
+
α
438
x
68
+
α
219
x
12
+
x
5
{\displaystyle x^{257}+\alpha ^{438}x^{68}+\alpha ^{219}x^{12}+x^{5}}
I 7
0
171430
,
2
64617
,
4
16842
,
6
5733
,
8
1932
,
10
483
,
12
105
,
14
21
,
16
147
,
18
105
,
20
154
,
22
21
,
24
42
{\displaystyle 0^{171430},2^{64617},4^{16842},6^{5733},8^{1932},10^{483},12^{105},14^{21},16^{147},18^{105},20^{154},22^{21},24^{42}}
9.17
x
80
+
α
73
x
66
+
x
17
+
α
73
x
10
+
x
3
{\displaystyle x^{80}+\alpha ^{73}x^{66}+x^{17}+\alpha ^{73}x^{10}+x^{3}}
B 31
0
160440
,
2
78834
,
4
17514
,
6
3388
,
8
777
,
10
483
,
12
126
,
14
49
,
16
21
{\displaystyle 0^{160440},2^{78834},4^{17514},6^{3388},8^{777},10^{483},12^{126},14^{49},16^{21}}
9.18
α
365
x
136
+
x
129
+
α
73
x
80
+
x
24
+
x
17
+
x
3
{\displaystyle \alpha ^{365}x^{136}+x^{129}+\alpha ^{73}x^{80}+x^{24}+x^{17}+x^{3}}
B 34
0
164199
,
2
76734
,
4
13524
,
6
4312
,
8
2205
,
12
147
,
16
294
,
18
147
,
20
49
,
22
21
{\displaystyle 0^{164199},2^{76734},4^{13524},6^{4312},8^{2205},12^{147},16^{294},18^{147},20^{49},22^{21}}
9.19
α
73
x
320
+
x
96
+
α
219
x
68
+
x
40
+
x
33
+
x
5
{\displaystyle \alpha ^{73}x^{320}+x^{96}+\alpha ^{219}x^{68}+x^{40}+x^{33}+x^{5}}
B 35
0
172557
,
2
68355
,
4
12201
,
6
3871
,
8
1638
,
10
735
,
12
1470
,
14
49
,
16
147
,
18
441
,
20
147
,
42
21
{\displaystyle 0^{172557},2^{68355},4^{12201},6^{3871},8^{1638},10^{735},12^{1470},14^{49},16^{147},18^{441},20^{147},42^{21}}
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