Abstract
It is shown in this paper that every correlation immune Boolean function of n variables can be written as f(x) = g(xG T ), where g is an algebraic non-degenerate Boolean function of k (k ≤ n) variables and G is a generating matrix of an [n, k, d] linear code. It is known that the correlation immunity of f (x) is at least d − 1. In this paper we further prove when the correlation immunity exceeds this lower bound. A method which can theoretically search exhaustively all possible correlation immune functions is proposed, while constructions of higher order correlation immune functions as well as algebraic non-degenerate correlation immune functions are discussed in particular. It is also shown that many cryptographic properties of g can be inherited by the correlation immune function f (x) = g(xG T) which is an important property for choosing useful correlation immune functions.
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© 1997 Springer-Verlag
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Dawson, E., Wu, CK. (1997). Construction of correlation immune Boolean functions. In: Han, Y., Okamoto, T., Qing, S. (eds) Information and Communications Security. ICICS 1997. Lecture Notes in Computer Science, vol 1334. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028473
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DOI: https://doi.org/10.1007/BFb0028473
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