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 | 2 | ^{[1]}^{[2]} | ||
Kasami | ^{[3]}^{[4]} | |||
Welch | ^{[5]} | |||
Niho | even | ^{[6]} | ||
odd | ||||
Inverse | ^{[2]}^{[7]} | |||
Dobbertin | ^{[8]} |
- ↑ Robert Gold, Maximal recursive sequences with 3-valued recursive cross-correlation functions (corresp.), IEEE transactions on Information Theory, 14(1):154-156, 1968
- ↑ ^{2.0} ^{2.1} Kaisa Nyberg, Differentially uniform mappings for cryptography, Workshop on the Theory and Application of Cryptographic Techniques, pp. 55-64, Springer, 1993
- ↑ Heeralal Janwa and Richard M Wilson, Hyperplane sections of Fermat varieties in in char. 2 and some applications to cyclic codes, International Symposium on Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes, pp. 180-194, Springer, 1993
- ↑ Tadao Kasami, The weight enumerators for several classes of subcodes of the 2nd order binary Reed-Muller codes, Information and Control, 18(4):369-394, 1971
- ↑ Hans Dobbertin, Almost perfect nonlinear power functions on : the Welch case, IEEE Transactions on Information Theory, 45(4):1271-1275, 1999
- ↑ Hans Dobbertin, Almost perfect nonlinear power functions on : the Niho case, Information and Computation, 151(1-2):57-72, 1999
- ↑ Thomas Beth and Cunsheng Ding, On almost perfect nonlinear permutations, Workshop on the Theory and Application of Cryptographic Techniques, pp. 65-76, Springer, 1993
- ↑ Hans Dobbertin, Almost perfect nonlinear power functions over : a new case for divisible by 5, Proceedings of the fifth conference on Finite Fields and Applications FQ5, pp.113-121