Verifiable Threshold Multiplication Protocol based on Oblivious Transfer

Abstract

Shamir Secrets Sharing (SSS) is a foundational element of many Multi-Party Computation (MPC) protocols. Although SSS has the ability to handle linear combinations of multiple secrets natively, its ability to handle the multiplication of secrets is limited. In general, the multiplication of secrets requires more participants, due to the increased “degree”. In this paper, we present a verifiable method for handling the multiplication of SSS without increasing its degree. Our method is based on the Gilboa Protocol or its variants, which are built on top of Oblivious Transfer (OT). We also provide a security analysis, demonstrating that the method is secure under the assumption of a malicious adversary security model. As an application use case, we present a new ECDSA threshold signature scheme built on top of our method.