Known infinite families of APN power functions over GF(2^n)
The following table provides a summary of all known infinite families of power APN functions of the form .
Family | Exponent | Conditions | Reference | |
---|---|---|---|---|
Gold | ^{[1]}^{[2]} | |||
Kasami | ^{[3]}^{[4]} | |||
Welch | ^{[5]} | |||
Niho | even | ^{[6]} | ||
odd | ||||
Inverse | ^{[2]}^{[7]} | |||
Dobbertin | ^{[8]} |
- ↑ Gold R. Maximal recursive sequences with 3-valued recursive cross-correlation functions. IEEE Trans. Inf. Theory. 1968;14(1):154-6.
- ↑ ^{2.0} ^{2.1} Nyberg K. Differentially uniform mappings for cryptography. InWorkshop on the Theory and Application of of Cryptographic Techniques 1993 May 23 (pp. 55-64).
- ↑ Janwa H, Wilson RM. Hyperplane sections of Fermat varieties in P 3 in char. 2 and some applications to cyclic codes. InInternational Symposium on Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes 1993 May 10 (pp. 180-194).
- ↑ Kasami T. The weight enumerators for several classes of subcodes of the 2nd order binary Reed-Muller codes. Information and Control. 1971 May 1;18(4):369-94.
- ↑ Dobbertin H. Almost perfect nonlinear power functions on : the Welch case. IEEE Transactions on Information Theory. 1999 May;45(4):1271-5.
- ↑ Dobbertin H. Almost perfect nonlinear power functions on : the Niho case. Information and Computation. 1999 May 25;151(1-2):57-72.
- ↑ Beth T, Ding C. On almost perfect nonlinear permutations. InWorkshop on the Theory and Application of of Cryptographic Techniques 1993 May 23 (pp. 65-76).
- ↑ Dobbertin H. Almost perfect nonlinear power functions on : a new case for n divisible by 5. InFinite Fields and Applications 2001 (pp. 113-121).