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Generalized perfectly nonlinear functions

In: Tatra Mountains Mathematical Publications, vol. 20, no. 3
Otokar Grošek - Ladislav Satko - Karol Nemoga
Detaily:
Rok, strany: 2000, 127 - 137
O článku:
It is well known that it is not possible to find a Boolean function $ f: Bbb Z2n ightarrow Bbb Z2m$ satisfying basic cryptologie criteria - balancedness and perfect nonlinearity — at the same time. The best approximation to this target was done by Nyberg in K. Nyberg: Perfect nonlinar S-boxes. Advances in Cryptology — Proceedings of Eurocrypt'90, in: Lecture Notes in Comput. Sci., Vol. 473, Springer-Verlag, Berlin, pp. 378 –386, 1990. In her construction she used slightly unbalanced functions, namely bent functions, providing $n=2k, n≥ 2m$. Such functions satisfy also a condition of the minimal mutual input/output information. In our contribution we show that a change of the domain (the group) $Z2n$ by a quasigroup, say $S$, enables to construct balanced as well as (generalized) perfectly nonlinear functions. Such functions have completely flat difference table.
Ako citovať:
ISO 690:
Grošek, O., Satko, L., Nemoga, K. 2000. Generalized perfectly nonlinear functions. In Tatra Mountains Mathematical Publications, vol. 20, no.3, pp. 127-137. 1210-3195.

APA:
Grošek, O., Satko, L., Nemoga, K. (2000). Generalized perfectly nonlinear functions. Tatra Mountains Mathematical Publications, 20(3), 127-137. 1210-3195.