A method and devices for securely and privately generating a threshold vault address and distributed individual key shares reliant upon individually selected polynomial functions, without revealing the key shares and without ever reconstructing the private key. A digital asset stored at the threshold vault address may be used as an input to a transaction through generating a digital signature corresponding to the threshold vault address. Methods and devices are described for collaboratively generating the digital signature without reconstructing the private key or revealing individual key shares. Methods and devices are described for refreshing the distributed private key shares.