# A Comment on Privacy-Preserving Scalar Product Protocols as proposed in "SPOC"

## TL;DR

This paper critically analyzes Lu et al.'s privacy-preserving scalar product protocol, demonstrating its insecurities and proving it cannot be secure without cryptographic assumptions, thus cautioning against its use.

## Contribution

It reveals the insecurity of a widely cited PPSP protocol and provides theoretical proof of its fundamental limitations without cryptographic assumptions.

## Key findings

- Lu et al.'s protocol is insecure against specific attacks.
- The protocol cannot be made secure without cryptographic assumptions.
- Impossibility results confirm inherent insecurity of the protocol.

## Abstract

Privacy-preserving scalar product (PPSP) protocols are an important building block for secure computation tasks in various applications. Lu et al. (TPDS'13) introduced a PPSP protocol that does not rely on cryptographic assumptions and that is used in a wide range of publications to date. In this comment paper, we show that Lu et al.'s protocol is insecure and should not be used. We describe specific attacks against it and, using impossibility results of Impagliazzo and Rudich (STOC'89), show that it is inherently insecure and cannot be fixed without relying on at least some cryptographic assumptions.