On the Cryptanalysis of Nonlinear Sequences [Invited Paper]
A nonlinear boolean function f(x1; x2; : : : ; xk) of k binary variables may be used in two basically different ways to generate a non-linear binary sequence, internally or externally. Internally, f may be part of the feedback computation of a nonlinear feedback shift register. Externally, f may be applied to the output bit stream of another sequence generator (e.g. a linear shift register) to introduce nonlinearity, or greater nonlinearity. A third approach is to use f to obtain a nonlinear combination of k linear sequences. The vulnerability of systems using f in any of these ways to cryptanalysis depends on the multidimensional correlations of f with the modulo 2 sums of the subsets of its variables. This principle was published by the present author in  in 1959, and included as Chapter 8 in his book  in 1967. It was subsequently rediscovered and republished in 1988 in , on the basis of which it is sometimes known as the Xiao-Massey algorithm. Some practical aspects of the use of this principle in code construction as well as code breaking, and for other types of signal design, are discussed.
KeywordsBoolean Function Binary Sequence Truth Table Shift Register Linear Sequence
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