Constructions of Efficiently Implementable Boolean Functions with Provable Nonlinearity/Resiliency/Algebraic Immunity Trade-Offs

• URL: http://arxiv.org/abs/2510.01720v2
• Date: Mon, 06 Oct 2025 15:57:51 GMT
• Title: Constructions of Efficiently Implementable Boolean Functions with Provable Nonlinearity/Resiliency/Algebraic Immunity Trade-Offs
• Authors: Palash Sarkar,
• Abstract summary: We describe several families of efficiently implementable Boolean functions.<n>The families achieve provable trade-offs between resiliency, nonlinearity, and algebraic immunity.
• Score: 1.6836789895924147
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We describe several families of efficiently implementable Boolean functions achieving provable trade-offs between resiliency, nonlinearity, and algebraic immunity. In particular, the following statement holds for each of the function families that we propose. Given integers $m_0\geq 0$, $x_0\geq 1$, and $a_0\geq 1$, it is possible to construct an $n$-variable function which has resiliency at least $m_0$, linear bias (which is an equivalent method of expressing nonlinearity) at most $2^{-x_0}$ and algebraic immunity at least $a_0$; further, $n$ is linear in $m_0$, $x_0$ and $a_0$, and the function can be implemented using $O(n)$ 2-input gates, which is essentially optimal.

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