We introduce, motivate and study \(\varepsilon \)-almost collision-flat universal (ACFU) hash functions \(f:\mathcal X\times \mathcal S\rightarrow \mathcal A\). Their main property is that the number of collisions in any given value is bounded. Each \(\varepsilon \)-ACFU hash function is an \(\varepsilon \)-almost universal (AU) hash function, and every \(\varepsilon \)-almost strongly universal (ASU) hash function is an \(\varepsilon \)-ACFU hash function. We study how the size of the seed set \(\mathcal S\) depends on \(\varepsilon ,|\mathcal X |\) and \(|\mathcal A |\). Depending on how these parameters are interrelated, seed-minimizing ACFU hash functions are equivalent to mosaics of balanced incomplete block designs (BIBDs) or to duals of mosaics of quasi-symmetric block designs; in a third case, mosaics of transversal designs and nets yield seed-optimal ACFU hash functions, but a full characterization is missing. By either extending \(\mathcal S\) or \(\mathcal X\), it is possible to obtain an \(\varepsilon \)-ACFU hash function from an \(\varepsilon \)-AU hash function or an \(\varepsilon \)-ASU hash function, generalizing the construction of mosaics of designs from a given resolvable design (Gnilke et al. in Des. Codes Cryptogr. 86(1):85–95, 2017). The concatenation of an ASU and an ACFU hash function again yields an ACFU hash function. Finally, we motivate ACFU hash functions by their applicability in privacy amplification.

我们介绍、激励和研究\(\varepsilon \) -几乎碰撞平坦通用 (ACFU) 哈希函数\(f:\mathcal X\times \mathcal S\rightarrow \mathcal A\)。它们的主要属性是任何给定值的碰撞次数都是有界的。每个\(\varepsilon \) -ACFU 哈希函数都是一个\(\varepsilon \) -几乎通用 (AU) 哈希函数，并且每个\(\varepsilon \) - 几乎强通用 (ASU) 哈希函数都是一个\(\ varepsilon \) -ACFU 哈希函数。我们研究种子集\(\mathcal S\)的大小如何取决于\(\varepsilon ,|\mathcal X |\)和\(|\mathcal A |\)。根据这些参数的相互关联方式，种子最小化 ACFU 哈希函数相当于平衡不完全块设计 (BIBD) 的马赛克或准对称块设计的马赛克的对偶；在第三种情况下，横向设计和网络的镶嵌产生种子最优 ACFU 哈希函数，但缺少完整的表征。通过扩展\(\mathcal S\)或\(\mathcal X\)，可以从\(\varepsilon \) -AU 哈希函数或 \(\varepsilon \) -AU 哈希函数获得\(\varepsilon \) -ACFU 哈希函数。 (\varepsilon \) -ASU 哈希函数，从给定的可解析设计中概括设计马赛克的构造（Gnilke et al. in Des. Codes Cryptogr. 86(1):85–95, 2017）。ASU 和 ACFU 哈希函数的串联再次产生 ACFU 哈希函数。最后，我们通过 ACFU 哈希函数在隐私放大方面的适用性来激励它们。