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\beginabstract This paper introduces the \textitBorellus connection, a novel theoretical link between Borell's inequality in Gaussian analysis and the algebraic structure of certain pseudorandom generators. We demonstrate that the Borellus transform—a composition of linear feedback shift registers (LFSRs) with nonlinear mixing—achieves provable guarantees on higher-order correlations. Our main result (Theorem 1) shows that any Boolean function with bounded Fourier tail must be pseudorandom against the Borellus construction. We provide explicit parameters, security proofs, and comparative performance metrics. The framework unifies concepts from probability (Borell–TIS inequality), coding theory (BCH bounds), and stream cipher design, opening new directions for post-quantum lightweight cryptography. \endabstract

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