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

Family	Exponent	Conditions	$\deg(x^{d})$	Reference
Gold	$2^{i}+1$	$\gcd(i,n)=1$	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

Navigation menu