In certain embodiments, shares related to an output of a function having multiple shares of a secret as input may be computed. In some embodiments, with respect to initial key shares of a key that are collectively held by multiple parties, an output of an arithmetic function (performed on an initial key share of the initial key shares) may be received from each of the multiple parties. The outputs from the multiple parties may be provided as input for a Multi-Party Computation (MPC) process, where the MPC process outputs final key shares in connection with the outputs from the multiple parties being provided as input for the MPC process. With respect to each party of the multiple parties, a final key share of the final key shares may be sent to the party.