Bifrost: A Much Simpler Secure Two-Party Data Join Protocol for Secure Data Analytics

TL;DR

Bifrost introduces a simple, redundancy-free secure two-party data join for vertically partitioned data by combining an ECC-based Private Set Intersection (ECDH-PSI) with a two-party oblivious shuffle and a dual-mapping optimization. This design replaces the heavy OPPRF and cuckoo-hashing components of prior work and yields a joined-table secret shared between parties, exposing only the joined-row count. The authors provide formal security proofs in the semi-honest model and demonstrate up to 22x online speedups and over 80% communication reductions on real-world datasets up to 100 GB, with downstream secure analytics showing substantial gains and accuracy preservation compared to CPSI. They also offer practical extensions for unaligned data, detailed evaluations across varying row counts and feature dimensions, and a clear path to stronger security against malicious adversaries. Overall, Bifrost delivers a scalable, performance-oriented solution for secure data analytics pipelines that rely on fast, redundancy-free secure joins.

Abstract

Secure data join enables two parties with vertically distributed data to securely compute the joined table, allowing the parties to perform downstream Secure multi-party computation-based Data Analytics (SDA), such as training machine learning models, based on the joined table. While Circuit-based Private Set Intersection (CPSI) can be used for secure data join, it introduces redundant dummy rows in the joined table, which results in high overhead in the downstream SDA tasks. iPrivJoin addresses this issue but introduces significant communication overhead in the redundancy removal process, as it relies on the cryptographic primitive OPPRF for data encoding and multiple rounds of oblivious shuffles. In this paper, we propose a much simpler secure data join protocol, Bifrost, which outputs (the secret shares of) a redundancy-free joined table. The highlight of Bifrost lies in its simplicity: it builds upon two conceptually simple building blocks, an ECDH-PSI protocol and a two-party oblivious shuffle protocol. The lightweight protocol design allows Bifrost to avoid the need for OPPRF. We also proposed a simple optimization named \textit{dual mapping} that reduces the rounds of oblivious shuffle needed from two to one. Experiments on datasets of up to 100 GB show that Bifrost achieves $2.54 \sim 22.32\times$ speedup and reduces the communication by $84.15\% \sim 88.97\%$ compared to the SOTA redundancy-free secure data join protocol iPrivJoin. Notably, the communication size of Bifrost is nearly equal to the size of the input data. In the two-step SDA pipeline evaluation (secure join and SDA), the redundancy-free property of Bifrost not only avoids the catastrophic error rate blowup in the downstream tasks caused by the dummy rows in the joined table (as introduced in CPSI), but also shows up to $2.80\times$ speed-up in the SDA process with up to $73.15\%$ communication reduction.

Figures (8)

• Figure 1: An example of a vertically distributed data setting. $P_a$ and $P_b$ each hold a table with three records. Both tables contain the intersection IDs "$bbb$" and "$ddd$".
• Figure 2: Simplified workflow of Bifrost with Dual Mapping optimization. The intersection IDs and their features are highlighted in bold. In the first step, both parties obtain mapped intersection indices $\pi_1(I)$ and $\pi_2(I)$. In the second step, both parties first obtain dual-shuffled feature shares $\langle {\pi_1(F^a)} \rangle$ and $\langle {\pi_2(F^b)} \rangle$ via one round of $\Pi_{\rm O\text{-}Shuffle}$, then both parties locally extract the shares of the joined table $\mathcal{D}$ from $\langle {\pi_1(F^a)} \rangle$ and $\langle {\pi_2(F^b)} \rangle$ according to $\pi_1(I)$ and $\pi_2(I)$.
• Figure 3: Ideal functionality of Secure Two-Party Data Join.
• Figure 4: Ideal functionality of SMIG.
• Figure 5: An illustration of constructing $\mathsf{MIPairs}$ by $P_a$ in Step 2-(1) of $\Pi_{\text{SMIG}}$ (Protocol \ref{['pro:smig']}), using the example data described at the beginning of Section \ref{['sec:design']}.

Theorems & Definitions (5)

• Definition 1: Semi-honest Model
• Theorem 1
• Theorem 2
• Theorem 3
• Theorem 1