Paper 2026/1626

Adaptive-Input-Secure Updatable Private Set Union

Abstract

In multi-epoch deployments, private set union~(PSU) operates in an adaptive-input loop: after observing the union at epoch $t$, the receiver may choose its next input for epoch $t+1$. Liu et al.~(EUROCRYPT 2026) formalized this multi-epoch adaptive-input setting for updatable private set intersection and provided an instantiation, but their framework does not extend to PSU. Meanwhile, existing PSU protocols are analyzed only in the single-shot setting. We present the first semi-honest, adaptive-input-secure updatable PSU protocol supporting two-sided add/delete updates in the multi-epoch adaptive-input setting of Liu et al. Our construction is built around a new primitive, the updatable oblivious key-value store (uOKVS). Its defining rule, distributional erasure, requires each refresh to be distributed identically to a fresh static encoding of the current key set, rather than merely indistinguishably. We realize uOKVS by combining the Band-OKVS of Bienstock et al. with a PRF under a persistent key. The resulting refresh reuses a cached factorization, so its per-epoch encoding cost scales linearly rather than quadratically in the band width $w$. Building on this layer, we obtain a multi-epoch PSU protocol whose leakage is limited to set and update cardinalities, even against adaptive-input adversaries. We implement the protocol and benchmark it in a single-threaded setting. At $n = 2^{20}$ with per-epoch updates $\Delta = 55$ over $10$ epochs, the online per-epoch wall-clock time is $1.41$ s on LAN, yielding a $30.9\times$--$98.9\times$ speedup over prior static PSU protocols re-executed from scratch at each epoch.