The Borellus Connection Pdf Better Guide

We bridge this gap by introducing the \textbfBorellus connection, where the nonlinear part of a stream cipher is interpreted as a threshold function applied to a Gaussian process. The main insight: if the underlying LFSR sequence has low ``Borellus complexity'', then the output resists fast correlation attacks.

\subsectionBorell–TIS inequality For any $t>0$, [ \Pr\left( \sup_s \in S X_s > \mathbbE[\sup X_s] + t \right) \le e^-t^2/(2\sigma^2), ] where $\sigma^2$ is the maximal variance of $X_s$. This controls the deviation of the threshold function's output.

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