Difference between revisions of "CCZ-equivalence of Families of APN Polynomials over GF(2^n) from the table (for n between 6 and 11)"

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m (Nikolay moved page CCZ-equivalence of Families of APN Polynomials over GF(2^n) from the table (for n is equal or larger than 6 and equal or smaller than 11) to [[CCZ-equivalence of Families of APN Polynomials over GF(2^n) from the table (for n betw...)
m
Line 14: Line 14:
  
 
<tr>
 
<tr>
<td><math>1</math></td>
+
<td>1</td>
 
<td><math>x^{2^s+1}+u^{2^k-1}x^{2^{ik}+2^{mk+s}}</math>
 
<td><math>x^{2^s+1}+u^{2^k-1}x^{2^{ik}+2^{mk+s}}</math>
 
<math>p=3</math>
 
<math>p=3</math>
Line 26: Line 26:
  
 
<tr>
 
<tr>
<td><math>2</math></td>
+
<td>2</td>
 
<td><math>x^{2^s+1}+u^{2^k-1}x^{2^{ik}+2^{mk+s}}</math>
 
<td><math>x^{2^s+1}+u^{2^k-1}x^{2^{ik}+2^{mk+s}}</math>
 
<math>p=4</math>
 
<math>p=4</math>
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<tr>
 
<tr>
<td><math>3</math></td>
+
<td>3</td>
 
<td><math>x^{2^{2i}+2^i}+bx^{q+1}+cx^{q(2^{2i}+2^i)}</math></td>
 
<td><math>x^{2^{2i}+2^i}+bx^{q+1}+cx^{q(2^{2i}+2^i)}</math></td>
 
<td>New</td>
 
<td>New</td>
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<tr>
 
<tr>
<td><math>4</math></td>
+
<td>4</td>
 
<td><math>x(x^{2^i}+x^q+cx^{2^iq})+x^{2^i}(c^qx^q+sx^{2^iq})+x^{(2^i+1)}q</math></td>
 
<td><math>x(x^{2^i}+x^q+cx^{2^iq})+x^{2^i}(c^qx^q+sx^{2^iq})+x^{(2^i+1)}q</math></td>
 
<td><math>N^\circ 3</math></td>
 
<td><math>N^\circ 3</math></td>
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<tr>
 
<tr>
<td><math>5</math></td>
+
<td>5</td>
 
<td><math>x^3+a^{-1}tr_n(a^3x^9)</math></td>
 
<td><math>x^3+a^{-1}tr_n(a^3x^9)</math></td>
 
<td>Gold<math>(a=1)</math>
 
<td>Gold<math>(a=1)</math>
Line 78: Line 78:
  
 
<tr>
 
<tr>
<td><math>6</math></td>
+
<td>6</td>
 
<td><math>x^3+a^{-1}tr_n^3(a^3x^9+a^6x^{18})</math></td>
 
<td><math>x^3+a^{-1}tr_n^3(a^3x^9+a^6x^{18})</math></td>
 
<td>Gold<math>(a=1)</math>
 
<td>Gold<math>(a=1)</math>
Line 91: Line 91:
  
 
<tr>
 
<tr>
<td><math>7</math></td>
+
<td>7</td>
 
<td><math>x^3+a^{-1}tr_n^3(a^6x^{18}+a^{12}x^{36})</math></td>
 
<td><math>x^3+a^{-1}tr_n^3(a^6x^{18}+a^{12}x^{36})</math></td>
 
<td>Gold<math>(a=1)</math>
 
<td>Gold<math>(a=1)</math>
Line 104: Line 104:
  
 
<tr>
 
<tr>
<td><math>8</math></td>
+
<td>8</td>
 
<td><math>ux^{2^s+1}+u^{2^k}x^{2^{-k}+2^{k+s}}+vx^{2^{-k}+1}+wu^{2^k+1} x^{2^{s}+2^{k+s}}</math>
 
<td><math>ux^{2^s+1}+u^{2^k}x^{2^{-k}+2^{k+s}}+vx^{2^{-k}+1}+wu^{2^k+1} x^{2^{s}+2^{k+s}}</math>
 
<math>v=0, w\ne0</math>
 
<math>v=0, w\ne0</math>
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<tr>
 
<tr>
<td><math>9</math></td>
+
<td>9</td>
 
<td><math>ux^{2^s+1}+u^{2^k}x^{2^{-k}+2^{k+s}}+vx^{2^{-k}+1}+wu^{2^k+1} x^{2^{s}+2^{k+s}}</math>
 
<td><math>ux^{2^s+1}+u^{2^k}x^{2^{-k}+2^{k+s}}+vx^{2^{-k}+1}+wu^{2^k+1} x^{2^{s}+2^{k+s}}</math>
 
<math>v\ne0, w=0</math>
 
<math>v\ne0, w=0</math>
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<tr>
 
<tr>
<td><math>10</math></td>
+
<td>10</td>
 
<td><math>ux^{2^s+1}+u^{2^k}x^{2^{-k}+2^{k+s}}+vx^{2^{-k}+1}+wu^{2^k+1} x^{2^{s}+2^{k+s}}</math>
 
<td><math>ux^{2^s+1}+u^{2^k}x^{2^{-k}+2^{k+s}}+vx^{2^{-k}+1}+wu^{2^k+1} x^{2^{s}+2^{k+s}}</math>
 
<math>v\ne0, w=0</math>
 
<math>v\ne0, w=0</math>
Line 145: Line 145:
  
 
<tr>
 
<tr>
<td><math>11</math></td>
+
<td>11</td>
<td><math>(x+x^{2^m})^{2^k+1}+u^{(2^{n}-1)/(2^m-1)}(u x+u^{2^m}x^{2^m})^{(2^k+1)2^i}+u(x+x^{2^m})(u x+u ^{2^m}x^{2^m})</math>
+
<td><math>(x+x^{2^m})^{2^k+1}+u^{(2^{n}-1)/(2^m-1)}(u x+u^{2^m}x^{2^m})^{(2^k+1)2^i}</math>
<td><math>-</math></td>
+
<math>+u(x+x^{2^m})(u x+u ^{2^m}x^{2^m})</math>
 +
<td>-</td>
 
<td>-</td>
 
<td>-</td>
 
<td>New <math>(i=2)</math>
 
<td>New <math>(i=2)</math>

Revision as of 15:45, 5 November 2019

CCZ-equivalence of Families of APN Polynomials over GF(2^n) from the table (for n is equal or larger than 6 and equal or smaller than 11)

Functions*
1

Gold - - - - -
2

- - - - - -
3 New - - - New I (

New II (

-
4 - New - : Case I

: Case II

-
5 Gold

New New I

New II

New New I

New II

New
6 Gold

- - New - -
7 Gold

- - New - -
8

New - - - - -
9

- - - - -
10

- - - - -
11

- - New

- - -