Structural Tightness of Quadratic Multi-Query Bounds for Universal Hashing: Applications to Accordion Modes

본문 미리보기

Universal hashing gives a pairwise guarantee: for two distinct messages, the probability of any fixed keyed-hash output difference is at most $\varepsilon$. Summing over the $\binom q2$ query pairs gives the familiar multi-query upper bound $\binom q2\varepsilon$, but this union bound does not show that one transcript can realize quadratically many useful pairwise events. We study when a single algebraically structured query set can do so by arranging many substantially different key condition