Extremal generalized S-boxes

被引:0
作者
Satko, L [1 ]
Grosek, O
Nemoga, K
机构
[1] Slovak Univ Technol Bratislava, Fac Elect Engn & Informat Technol, Bratislava 81219, Slovakia
[2] Slovak Univ Technol Bratislava, Math Inst, Bratislava 81219, Slovakia
[3] Slovak Acad Sci, Inst Math, Bratislava 81473, Slovakia
关键词
quasigroups; linear structures; Boolean functions; perfect nonlinearity;
D O I
暂无
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
It is well known that there does not exist a Boolean function f : Z(2)(m) --> Z(2)(n) satisfying both basic cryptologic criteria, balancedness and perfect nonlinearity. In [9] it was shown that, if we use as a domain quasigroup G instead of the group Z(2)(n), one can find functions which are at the same time balanced and perfectly nonlinear. Such functions have completely flat difference table. We continue in our previous work, but we turn our attention to the worst case when all lines of Cayley table of G define so called linear structure of f ([5]). We solve this problem in both directions: We describe all such bijections f : G --> Z(2)(n), for a given quasigroup \G\ = 2(n), and describe such quasigroups for a given function f.
引用
收藏
页码:85 / 99
页数:15
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