Methods are described for constructing a secret key by multiple participants from multiple ciphertexts such that any quorum combination of participants can decrypt their respective ciphertexts and so generate a fixed number of key fragments that can be combined by a recipient to generate the secret key. Worked examples are described showing how the encryption keys for the ciphertexts may be key wrapped using a key encapsulation mechanism for which ciphers that are resistant to attack by a quantum computer may be used. In these cases, a post-quantum quorum system is realised. Methods are described by which the quorum key fragment ciphertexts may be updated so that the original key fragments become invalid without necessitating any change to the secret key.