Mompe: Multiparty Oblivious Multivariate Polynomial Evaluation

This paper proposes a novel Multiparty Oblivious Multivariate Polynomial Evaluation (MOMPE) protocol, which enables secure multivariate polynomial computation among multiple parties for the first time. Unlike traditional Oblivious Polynomial Evaluation (OPE) protocols limited to two-party secure computation, MOMPE divides participating parties into a sender holding the multivariate polynomial <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$P$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$n$</tex> receivers, each holding a secret value <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\alpha_{i}$</tex> corresponding to a variable in <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$P$</tex>. Upon completion, the receivers learn <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$P\left(\alpha_{1}, \alpha_{2}, \ldots, \alpha_{n}\right)$</tex>, while the sender learns nothing. Assuming no collusion between the sender and receivers, we demonstrate MOMPE's security under the stringent Universal Composability (UC) framework, ensuring it remains secure in complex multiparty interactive environments. Our implementation and experiments validate MOMPE's performance, showing significantly less time consumption than the state-of-the-art Overdrive protocol for multiparty multivariate polynomial computation, while maintaining similar efficiency to OPE for participating parties. MOMPE has extensive application potential in privacy-preserving machine learning and collaborative data analysis, where multiple parties need to compute and analyze data together while protecting privacy. MOMPE offers a secure and efficient method for parties to utilize data without revealing sensitive information, opening new possibilities for privacy-preserving data collaboration and analysis.