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The output bits of this process are $\mathbb{Z}_2$-linear functions of the input bits. Specifically, if you write $x_1, x_2$ as column vectors of bits, then $$ \begin{bmatrix} x'_1 \\ x'_2 \end{bmatrix} = \left[ \begin{array}{cccc|cccc} 0 & 0 &\cdots & 0 & 1 & 0 & \cdots & 0 \\ 0 & 0 &\cdots & 0 ...


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Given some output of unknown seeds after an unknown number of steps, is it "computationally hard" to find a pair of seeds that produce the given output after a number of steps? Nope; two observations: With two successive outputs, you can compute the internal state; if you see the outputs $y_1, y_2$, then the internal state immediately after the ...


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