On Partial Anonymity in Secret Sharing

Anonymous secret sharing schemes allow a secret to be recovered from shares regardless of the identity of shareholders. Besides being interesting in its own right, this property is especially appealing to guarantee the anonymity of participants when secret sharing is used as a building block of more general distributed protocols (e.g. to anonymously share the secret key corresponding to a public key). However, current constructions of anonymous secret sharing schemes are not very efficient (because of the number of shares that every participant must hold) and existing bounds do not leave much room for optimism. In this paper we propose to weaken the anonymity condition to partial anonymity, where by partial anonymity we mean that the identity of the participant is not made public, but he is known to belong to some subset. That is, the search for a participant narrows down to one in a set of possible candidates. Furthermore, we propose a general construction of partial anonymous secret sharing schemes.