arXiv:2610.41369v1 Announce Type: new Abstract: A recurring step in two-party collaborative workflows combines a private candidate frontier with a partner's compatible evidence, scores the resulting candidates, and retains only a small frontier. Direct execution can expose intermediate candidates, local scores, or unauthorized evidence provenance. Existing MPC platforms and PSI protocols provide useful building blocks, but they do not define a unified post-alignment boundary for bounded-slot aggregation, fail-closed overflow handling, retained-frontier selection, and downstream disclosure. We present BlindStep, a fixed-shape MPC-online kernel for one such post-alignment step between two semi-honest parties. Given a frontend realizing the bounded-slot contract and an application enforcing the reveal policy $\rho$, BlindStep provides a per-invocation simulation-based guarantee in the $F_{\mathrm{align}}$-hybrid model: the kernel leaks only public setup parameters, fixed execution-shape metadata, a global overflow bit, and $\rho$-authorized Layer-2 disclosures. The guarantee excludes malicious security and multi-invocation composition, and treats frontend leakage and offline preprocessing separately. Within this kernel boundary, we implement six semi2k realizations in MP-SPDZ, crossing two sharing styles and three top-K strategies: H-variants compare over arithmetic shares, while B-variants convert packed ranking values to Boolean shares before selection. Under LAN, B-Queue is 6-7 times faster and uses about 40 times less communication than H-Queue at N = 256 and 2048. Against H-Sort on the same backend, B-Queue achieves speedups of 21 and 30 times and communication reductions of 204 and 290 times at N = 2048 and 8192, respectively. Under the evaluated N = 256, 100 ms RTT WAN profile, H-Sort becomes fastest, showing that round complexity can dominate backend choice for the measured MPC-online kernel.