Key generation using multiple sets of secret shares

A cryptographic method, including generating, using a meta-secret, a first plurality of cryptographic keys, each cryptographic key associated with a respective key identifier, creating, using the meta-secret, a second plurality of sets of secret-shares, which are capable, by combining all the secrets-shares in any one of the sets together with the respective key identifier, of generating the associated cryptographic key, and performing cryptographic operations using the cryptographic keys. Related methods and apparatus are also included.