The Security analysis and construction of correlation immune function with higher nonlinearity on stream cipher
Jeong-Mo Yang · Information Security and Cryptology · 2007
There are various methods constructing correlation immune functions such as Siegenthaler's, Camion et al's and Seberry et al's. In particular, Soberry et al's is a method which directly constructs balanced correlation immune functions of any order using the theory of Hadamard matrices. In this paper, we have studied Seberry et al's method for constructing a correlation immune function on a higher dimensional space by combining known correlation immune functions on a lower dimensional space. Futhermore, we calculated the nonlinearity of functions which are constructed by combining of several correlation immune functions. That is, we have shown that the direct sum of two correlation immune functions and a combination of four correlation immune functions have higher nonlinearity in comparison with each functions. This functions in stream cipher are safe against correlation attacks.