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