--------------------------------

From Boolean

CCZ-inequivalent APN Functions over 𝔽2n from the Known APN Classes for 6⩽n⩽11


N∘ Fanctions Equivalent to
6.1

6.2

6.3
x3

x24+ax17+a8x10+ax9+x3

ax3+x17+a4x24
Gold

C3

C7−C9
7.1

7.2

7.3

7.4

7.5

7.6

7.7
x3

x5

x9

x13

x57

x63

x3+Tr7(x9)
Gold

Gold

Gold

Kasami

Kasami

Inverse

C4
8.1

8.2

8.3

8.4

8.5

8.6

8.7
x3

x9

x57

x3+x17+p48x18+p3x33+px34+x48

x3+Tr8(x9)

x3+a−1Tr8(a3x9)

a(x+x16)(ax+a16x16)+a17(ax+a16x16)12
Gold

Gold

Kasami

C3

C4

C4

C10
9.1

9.2

9.3

9.4

9.5

9.6

9.7

9.8

9.9

9.10

9.11
x3

x5

x17

x13

x241

x19

x255

x3+Tr9(x9)

x3+Tr93(x9+x18)

x3+Tr93(x18+x36)

x3+a246x10+a47x17+a181x66+a428x129
Gold

Gold

Gold

Kasami

Kasami

Welch

Inverse

C4

C5

C6

C11
10.1

10.2

10.3

10.4

10.5

10.6

10.7

10.8
10.1

x3

x9

x57

x339

x6+x33+p31x192

x3+x72+p31x258

x3+Tr10(x9)

x3+a−1Tr10(a3x9)
Gold

Gold

Kasami

Dobbertin

C3

C3

C4

C4
11.1

11.2

11.3

11.4

11.5

11.6

11.7

11.8

11.9

11.10

11.11

11.12

11.13
x3

x5

x9

x17

x33

x13

x57

x241

x993

x35

x287

x123

x3+Tr11(x9)
Gold

Gold

Gold

Gold

Gold

Kasami

Kasami

Kasami

Kasami

Welch

Niho

Inverse

C4