Secret Sharing for Secure Model Parameter Determination

The patent divides the Hessian matrix into multiple shares distributed among different parties. Each party holds only a portion (share) of the Hessian matrix, and no single party can reconstruct the complete Hessian matrix or derive the original data. This segmentation allows Newton's method to be applied using distributed computations while preserving data privacy, as the complete information is never exposed to any single entity.

The patent introduces a secret sharing mechanism as an intermediary between the data parties and the optimization process. Instead of directly sharing sensitive data or complete Hessian matrices, parties share encrypted portions through the secret sharing protocol. This intermediary layer enables collaborative computation of Newton's method while preventing direct access to private data, thus resolving the contradiction between optimization speed and privacy protection.

The Hessian matrix is segmented into multiple shares that are distributed across parties. Each party performs computations on their local share without needing to handle the complete matrix. This segmentation reduces the computational burden on individual parties and decreases communication overhead, as only share updates need to be exchanged rather than complete matrix transmissions.

The patent applies partial action by having each party compute and share only the necessary portions (shares) of the Hessian matrix required for the distributed Newton's method. Rather than exchanging complete matrices, parties perform computations on their partial information and combine results through secure multiparty computation, reducing overall computational complexity while maintaining optimization accuracy.

The patent segments the modeling process into distributed computations that each enterprise can perform independently on their local data. The secret sharing mechanism divides model parameters and intermediate computations into shares that remain with respective parties. This segmentation enables robust cooperative modeling across multiple enterprises while simplifying coordination, as each party follows the same protocol steps without needing complex inter-party communication or data sharing.

Each enterprise performs computations on their own data and shares using their own computational resources. The distributed Newton's method allows parties to independently compute gradients and Hessian shares from their local data, then combine results through standardized secret sharing operations. This self-service approach improves model robustness through diverse data contributions while reducing coordination difficulty, as enterprises autonomously execute their portion of the workflow.