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

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<td><math>m+2</math></td>
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Revision as of 14:56, 4 January 2019

Some APN functions CCZ-equivalent to Gold functions and EA-inequivalent to power functions over[math]\displaystyle{ \mathbb{F}_{2^n} }[/math] (constructed in [1])

Functions Conditions [math]\displaystyle{ d^\circ }[/math]
[math]\displaystyle{ x^{2^i+1}+(x^{2^i}+x+tr_n(1)+1)tr_n(x^{2^i+1}+x\ tr_n(1)) }[/math] [math]\displaystyle{ n\geqslant4 }[/math]\ , [math]\displaystyle{ \gcd(i,n)=1 }[/math] [math]\displaystyle{ 3 }[/math]
[math]\displaystyle{ [x+tr_{n/3}(x^{2(2^i+1)}+x^{4(2^i+1)})+tr_n(x)tr_{n/3}(x^{2^i+1}+x^{2^{2i}(2^i+1)})]^{2^i+1} }[/math] [math]\displaystyle{ 6|n\ , \gcd(i,n)=1 }[/math] [math]\displaystyle{ 4 }[/math]
[math]\displaystyle{ 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] [math]\displaystyle{ m\ne n\ , n\ odd\ , m|n\ , \gcd(i,n)=1 }[/math] [math]\displaystyle{ m+2 }[/math]
  1. Budaghyan, Lilya, Claude Carlet, and Alexander Pott. "New classes of almost bent and almost perfect nonlinear polynomials." IEEE Transactions on Information Theory 52.3 (2006): 1141-1152.