Difference between revisions of "Some APN functions CCZ-equivalent to Gold functions and EA-inequivalent to power functions over GF(2^n)"

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<td><math>x^{2^i+1}+tr_{n/m}(x^{2^i+1})+x^{2^i}tr_{n/m}(x)+x \ tr_{n/m}(x)^{2^i}+[tr_{n/m}(x)^{2^i+1}+tr_{n/m}(x^{2^i+1})+tr_{n/m}(x)]^{\frac{1}{2^i+1}}(x^{2^i}+tr_{n/m}(x)^{2^i}+1)+[tr_{n/m}(x)^{2^i+1}+tr_{n/m}(x^{2^i+1})+tr_{n/m}(x)]^{\frac{2^i}{2^i+1}}(x+tr_{n/m}(x))</math></td>
+
<td><math>x^{2^i+1}+tr_{n/m}(x^{2^i+1})+x^{2^i}tr_{n/m}(x)+x \ tr_{n/m}(x)^{2^i}</math>
<td><math>m\ne n\ , n\ odd\ , m|n\ , \gcd(i,n)=1</math></td>
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<math>+[tr_{n/m}(x)^{2^i+1}+tr_{n/m}(x^{2^i+1})+tr_{n/m}(x)]^{\frac{1}{2^i+1}}(x^{2^i}+tr_{n/m}(x)^{2^i}+1)</math>
<td><math>m+2</math></td>
+
<math>+[tr_{n/m}(x)^{2^i+1}+tr_{n/m}(x^{2^i+1})+tr_{n/m}(x)]^{\frac{2^i}{2^i+1}}(x+tr_{n/m}(x))</math></td>
 +
<td><math>\ m\ne n\ , n\ odd\ , m|n\ , \gcd(i,n)=1\ </math></td>
 +
<td><math>\ m+2\ </math></td>
 
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Revision as of 15:52, 5 November 2019

Some APN functions CCZ-equivalent to Gold functions and EA-inequivalent to power functions over (constructed in [1])

Functions Conditions
,

  1. Budaghyan L, Carlet C, Pott A. New classes of almost bent and almost perfect nonlinear polynomials. IEEE Transactions on Information Theory. 2006 Mar;52(3):1141-52.