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

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<td><math>x^3+a^{-1} \mathrm{Tr}_n^3(a^6x^{18}+a^{12}x^{36})</math></td>
 
<td><math>x^3+a^{-1} \mathrm{Tr}_n^3(a^6x^{18}+a^{12}x^{36})</math></td>
 
<td> <math>3|n, a \ne 0</math></td>
 
<td> <math>3|n, a \ne 0</math></td>
<td><ref name="2_ref" />
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<td><ref name="2_ref" /></td>
 
</tr>
 
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Revision as of 14:27, 22 February 2019

Functions Conditions References
C1-C2 [1]
C3 , s.t. [2]
C4 [3]
C5 , [4]
C6 [4]
C7-C9 [5]
C10 even, and even, [6]
C11 satisfies the conditions in Lemma 8 of [7] [7]
  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. On Isotopic Construction of APN Functions. SETA 2018