Private Multi-party Matrix Multiplication and Trust Computations

TL;DR

This paper introduces new protocols for secure distributed matrix multiplication where each participant learns only a specific output row, improving efficiency and security in trust evaluations over networks.

Contribution

It presents a novel, efficient protocol for multi-party matrix multiplication with enhanced security features and practical trust evaluation applications.

Findings

Improved weighted average protocol with quadratic communication volume

A five-round protocol using homomorphic encryption secure against semi-honest and malicious adversaries

Verification of security using ProVerif and countermeasures for identified attacks

Abstract

This paper deals with distributed matrix multiplication. Each player owns only one row of both matrices and wishes to learn about one distinct row of the product matrix, without revealing its input to the other players. We first improve on a weighted average protocol, in order to securely compute a dot-product with a quadratic volume of communications and linear number of rounds. We also propose a protocol with five communication rounds, using a Paillier-like underlying homomorphic public key cryptosystem, which is secure in the semi-honest model or secure with high probability in the malicious adversary model. Using ProVerif, a cryptographic protocol verification tool, we are able to check the security of the protocol and provide a countermeasure for each attack found by the tool. We also give a randomization method to avoid collusion attacks. As an application, we show that this protocol enables a distributed and secure evaluation of trust relationships in a network, for a large class of trust evaluation schemes.