MPC Signing Group Re-Sharing Without Secret Key Reconstruction
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing multi-party computation (MPC) systems face inefficiencies and security risks when adding or removing users from a signing group, as traditional methods require a trusted party to reconstruct the secret key, exposing it to central points of failure and undermining security.
Innovation Solution
A decentralized method for managing MPC signing groups by re-sharing cryptographic keys among users using bivariate polynomials, allowing users to agree on new shares without exposing the underlying key, thus maintaining security and adaptability without group deletion.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If traditional methods are used to add or remove users from a signing group, then the signing group can be modified, but a trusted party must reconstruct the secret key which exposes it to central points of failure and undermines security
Solution Approach 1:
The secret key is segmented into multiple shares distributed among different users in the signing group. When modifying the group, only the shares of affected users are updated, while other users' shares remain valid. This segmentation eliminates the need for a trusted party to reconstruct the entire key, as each user operates independently on their own share.
Solution Approach 2:
A server acts as an intermediary to facilitate the share update process. The server receives requests to add or remove users, coordinates the update of affected shares using bivariate polynomials, and distributes the updated shares to relevant users. This intermediary enables decentralized key management without requiring any single user to hold the complete key.
2Adaptability or versatility
If the signing group is deleted and reformed when adding or removing users, then the group composition is updated, but time is lost and efficiency is reduced
Solution Approach 1:
The system pre-establishes a framework using bivariate polynomials that allows for efficient share updates without group deletion. Users are equipped with the necessary mathematical tools and protocols in advance, enabling them to perform share updates quickly and efficiently when group composition changes are needed.
Solution Approach 2:
The system changes the parameters of the polynomial shares rather than deleting and recreating the entire group. By updating the share values and polynomial coefficients for affected users while maintaining the overall group structure and threshold requirements, the system achieves flexible composition changes with minimal time loss.
3Ease of manufacture
If a trusted party reconstructs the secret key for group modifications, then the key can be updated, but the key is exposed to central points of failure
Solution Approach 1:
The users perform the key update operation themselves through their own shares. Each user who needs to be added or removed actively participates in the share update process by providing their share values and receiving updated shares. This self-service mechanism eliminates the need for a trusted third party to reconstruct the key, thereby removing the exposure to central points of failure.
Solution Approach 2:
The system transitions from a static key structure to a dynamic share update mechanism. The secret key remains distributed and unchanged at the group level, while individual shares are dynamically updated for affected users. This dynamic approach allows for easy key updates without centralization, as the key material flows through decentralized polynomial operations.
Data Source
AI summary
The disclosed technology provides for adjusting a quantity of users in a signing group for authorizing transactions utilizing multi-party-computation (MPC). A method can include receiving, by a server from a first signing client device amongst signing client devices in a signing group, a request to add or remove a signing client device from the group, the group including a polynomial designating a first threshold of devices required to authorize a transaction using respective shares of a cryptographic key, transmitting, to each remaining device in the group, a request for authorizing the request, receiving, from each, authorization of the request, initiating communication amongst a modified group of devices resulting from the authorization to generate new shares of the cryptographic key based on a bivariate polynomial having a second threshold signing requirement different from the first threshold, authenticating the new shares using the second threshold, and returning authentication of the new shares.