System and method for processing a shared secret

A method of constructing parts of a secret, which must be performed within a network comprising multiple computing devices, each arranged to securely store at least a part of a secret k for which n shares are required to reconstruct the secret and which may be provided access reliably a number m of said parts at any given time, the method comprising the steps of: determining n shares for a scheme for sharing secrets n n, each part comprising a value and ; storing at least some of said parts in said computing devices such that at least m of said n shares are reliably accessible; determining the shared secret k according to said shares y; characterized by m being less than n and by the steps of: determining a new (nm) shares consistent with the shared secret k and the parties; and store the additional parts in an accessible place reliably.