Systems and methods for securely adding and removing users from a signing group for key-based transactions in multi-party computation systems

A system for adjusting a quantity of users in a signing group for authorizing transactions utilizing multi-party-computation (MPC) across a network, the system comprising:

• a plurality of signing client devices;
• and
• a server in wireless network communication with the plurality of signing client devices, wherein the server is configured to:
• receive, from a first signing client device amongst the plurality of signing client devices included in a signing group, a request to add or remove at least one signing client device from the signing group, wherein the signing group includes a polynomial designating a first threshold of signing client devices in the signing group that is required to authorize a transaction using respective shares of a cryptographic key;
• transmit, to each remaining signing client device in the signing group, a request for authorizing the request to add or remove the at least one signing client device from the signing group;
• receive, from each remaining signing client device in the signing group, authorization of the request to add or remove the at least one signing client device from the signing group, wherein a modified signing group including a modified group of signing client devices results from the authorization of the request;
• initiate, in response to receiving the authorization from each remaining signing client device, communication amongst the modified group of signing client devices to generate new shares of the cryptographic key, wherein generating the new shares of the cryptographic key comprises:
• computing a bivariate polynomial that has a second threshold signing requirement different from the first threshold, wherein the bivariate polynomial further comprises a constant coefficient that is shared amongst two univariate polynomials, wherein the two univariate polynomials are derived from the polynomial associated with the first threshold and the signing group, and
• dynamically generating group authentication information associated with the modified group of signing client devices that includes the bivariate polynomial and the second threshold;
• authenticate the new shares using the second threshold;
• and
• return authentication of the new shares of the cryptographic key.