A Response to: A Note on "Privacy Preserving n-Party Scalar Product Protocol"

TL;DR

This paper defends the privacy-preserving $n$-party scalar product protocol by clarifying its security model and operational mechanics. It shows that transforming the input vectors into diagonal matrices and applying the trace map $\varphi$ with delegated secret sharing and sub-protocols preserves privacy, and it provides a concrete defense against a proposed semi-honest server attack. The authors acknowledge the exponential time complexity but argue that the protocol remains usable in vertically partitioned federated learning scenarios with relatively few parties, supported by follow-up work demonstrating practical runtimes. The discussion reframes the protocol's applicability, outlining its intended use cases (e.g., population subset queries) and clarifying misunderstandings that led to perceived insecurity or impracticality. Overall, the work reinforces that the protocol can be a safe, purpose-built tool in privacy-preserving collaborative settings, provided its limitations are respected.

Abstract

We reply to the comments on our proposed privacy preserving n-party scalar product protocol made by Liu. In their comment Liu raised concerns regarding the security and scalability of the $n$-party scalar product protocol. In this reply, we show that their concerns are unfounded and that the $n$-party scalar product protocol is safe for its intended purposes. Their concerns regarding the security are based on a misunderstanding of the protocol. Additionally, while the scalability of the protocol puts limitations on its use, the protocol still has numerous practical applications when applied in the correct scenarios. Specifically within vertically partitioned scenarios, which often involve few parties, the protocol remains practical. In this reply we clarify Liu's misunderstanding. Additionally, we explain why the protocols scaling is not a practical problem in its intended application.