Abstract: A method of constructing shares in a secret is disclosed. The method operates in a network comprising a number of computing devices, each arranged to securely store at least one share in the secret k for which n shares are required to reconstruct the secret and to which access to a number m of the shares can be reliably provided at any given time. The method comprises the steps of: determining n shares for an n-of-n secret sharing scheme, each share comprising a value y; storing at least some of the shares in the computing devices such that at least m of the n shares are reliably accessible; determining the shared secret k according to the shares y; determining a further (n-m) shares consistent with the shared secret k and the shares y; and storing the additional shares in a reliably accessible location.