Difference between revisions of "Known infinite families of quadratic APN polynomials over GF(2^n)"

From Boolean Functions
Jump to: navigation, search
m
m
Line 62: Line 62:
 
<td>C11</td>
 
<td>C11</td>
 
<td><math>L(x)^{2^i}x+L(x)x^{2^i}</math></td>
 
<td><math>L(x)^{2^i}x+L(x)x^{2^i}</math></td>
<td><math>n=km, \gcd(n,i)=1, L(x)=\sum_{j=0}^{k-1}a_jx^{2^{jm}}</math> satisfies the conditions in Theorem 3.6 of [7]</td>
+
<td><math>n=km, m>1, \gcd(n,i)=1, L(x)=\sum_{j=0}^{k-1}a_jx^{2^{jm}}</math> satisfies the conditions in Theorem 3.6 of [7]</td>
 
<td><ref>Villa I, Budaghyan L, Calderini M, Carlet C, Coulter R. Constructing APN functions through isotopic shift. Cryptology ePrint Archive, Report 2018/769</ref></td>
 
<td><ref>Villa I, Budaghyan L, Calderini M, Carlet C, Coulter R. Constructing APN functions through isotopic shift. Cryptology ePrint Archive, Report 2018/769</ref></td>
 
</tr>
 
</tr>

Revision as of 16:20, 9 January 2020

Functions Conditions References
C1-C2 , [1]
C3 , [2]
C4 [3]
C5 , [4]
C6 [4]
C7-C9 , [5]
C10 even, and even, [6]
C11 satisfies the conditions in Theorem 3.6 of [7] [7]
C12 , [8]
C13 [9]
,
  1. Budaghyan L, Carlet C, Leander G. Two classes of quadratic APN binomials inequivalent to power functions. IEEE Transactions on Information Theory. 2008 Sep;54(9):4218-29.
  2. Budaghyan L, Carlet C. Classes of quadratic APN trinomials and hexanomials and related structures. IEEE Transactions on Information Theory. 2008 May;54(5):2354-7.
  3. Budaghyan L, Carlet C, Leander G. Constructing new APN functions from known ones. Finite Fields and Their Applications. 2009 Apr 1;15(2):150-9.
  4. 4.0 4.1 Budaghyan L, Carlet C, Leander G. On a construction of quadratic APN functions. InInformation Theory Workshop, 2009. ITW 2009. IEEE 2009 Oct 11 (pp. 374-378). IEEE.
  5. Bracken C, Byrne E, Markin N, Mcguire G. A few more quadratic APN functions. Cryptography and Communications. 2011 Mar 1;3(1):43-53.
  6. Zhou Y, Pott A. A new family of semifields with 2 parameters. Advances in Mathematics. 2013 Feb 15;234:43-60.
  7. Villa I, Budaghyan L, Calderini M, Carlet C, Coulter R. Constructing APN functions through isotopic shift. Cryptology ePrint Archive, Report 2018/769
  8. Taniguchi H. On some quadratic APN functions. Des. Codes Cryptogr. 2019, https://doi.org/10.1007/s10623-018-00598-2
  9. Budaghyan L, Helleseth T, Kaleyski N. A new family of APN quadrinomials. Cryptology ePrint Archive, Report 2019/994