Combinatorial Privacy: Private Multi-Party Bitstream Grand Sum by Hiding in Birkhoff Polytopes

ArXi:2603.22808v1 Announce Type: cross We develop a finite-sample $(\varepsilon,\delta)$-DP analysis with explicit constants. In the full variant, where the aggregator sees a doubly stochastic matrix per client, the log-Lipschitz constant grows as $n^4 K_t$ and a signal-to-noise analysis shows the DP guarantee is non-vacuous only when the private signal is undetectable.