Known inifinte families of quadratic APN polynomials over GF(2^n): Difference between revisions
Jump to navigation
Jump to search
(Created page with "<table> <tr> <th><math>N^\circ</math></th> <th>Functions</th> <th>Conditions</th> <th>References</th> </tr> </table>") |
mNo edit summary |
||
| Line 5: | Line 5: | ||
<th>Conditions</th> | <th>Conditions</th> | ||
<th>References</th> | <th>References</th> | ||
</tr> | |||
<tr> | |||
<td>C1-C2</td> | |||
<td><math>x^{2^s+1}+u^{2^k-1}x^{2^{ik}+2^{mk+s}}</math></td> | |||
<td><math>n = pk, \gcd(k,3) = \gcd(s,3k) = 1, p \in \{3,4\}, i = sk \mod p, m = p -i, n \ge 12, u \text{ primitive in } \mathbb{F}_{2^n}^*</math></td> | |||
<td><ref>L. Budaghyan, C. Carlet, G. Leander, ''Two Classes of Quadratic APN Binomials Inequivalent to Power Functions'', IEEE Trans. Inform. Theory 54(9), 2008, pp. 4218-4229</ref> | |||
</tr> | </tr> | ||
</table> | </table> | ||
Revision as of 11:57, 5 December 2018
| [math]\displaystyle{ N^\circ }[/math] | Functions | Conditions | References |
|---|---|---|---|
| C1-C2 | [math]\displaystyle{ x^{2^s+1}+u^{2^k-1}x^{2^{ik}+2^{mk+s}} }[/math] | [math]\displaystyle{ n = pk, \gcd(k,3) = \gcd(s,3k) = 1, p \in \{3,4\}, i = sk \mod p, m = p -i, n \ge 12, u \text{ primitive in } \mathbb{F}_{2^n}^* }[/math] | [1] |
- ↑ L. Budaghyan, C. Carlet, G. Leander, Two Classes of Quadratic APN Binomials Inequivalent to Power Functions, IEEE Trans. Inform. Theory 54(9), 2008, pp. 4218-4229