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Let $m = 1 + \log \ell$. Identify a hash function $h \colon \{0, 1\}^k \to \{0, 1\}^m$ with its $n$-bit truth table $h \in \{0, 1\}^n$ where $n = m \cdot 2^k$. Our hash family $\mathcal{H} \subseteq \{0, 1\}^n$ consists of an $\varepsilon$-biased set for a suitable $\varepsilon = \ell^{-\Theta(k)}$. Explicit constructions of such a hash family are known with ...


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