Known infinite families of APN power functions over GF(2^n)

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Family	Exponent	Conditions	[math]\displaystyle{ \deg(x^d) }[/math]	Reference
Gold	[math]\displaystyle{ 2^i + 1 }[/math]	[math]\displaystyle{ \gcd(i,n) = 1 }[/math]	2	^[1]^[2]

↑ Robert Gold, Maximal recursive sequences with 3-valued recursive cross-correlation functions (corresp.), IEEE transactions on Information Theory, 14(1):154-156, 1968
↑ Kaisa Nyberg, Differentially uniform mappings for cryptography, Workshop on the Theory and Application of Cryptographic Techniques, pp. 55-64, Springer, 1993

[1] Robert Gold, Maximal recursive sequences with 3-valued recursive cross-correlation functions (corresp.), IEEE transactions on Information Theory, 14(1):154-156, 1968

[2] Kaisa Nyberg, Differentially uniform mappings for cryptography, Workshop on the Theory and Application of Cryptographic Techniques, pp. 55-64, Springer, 1993

[1]

[2]

Known infinite families of APN power functions over GF(2^n)

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