A Quantum Evolving Secret Sharing Scheme

An evolving secret sharing scheme is supposed to accommodate unbounded number (potentially infinite) of new participants over time and the dealer should not know the set of participants in advance. In this paper we initiate the study of quantum evolving schemes to share a quantum secret and show how to construct such a scheme where the qualified subsets (the sets which can reconstruct the secret) of participants are of increasing size as the number of participants increases with time. Share is given to new participants without modifying shares of old participants. While quantum secret sharing schemes which can accommodate new participants over time have been constructed before, a quantum scheme which can handle an unbounded and unspecified number of participants has not been considered so far. We also discuss the resilience of our scheme against a bounded number of quantum queries by an adversary/eavesdropper. This is achieved by using special functions for which lower bounds on their quantum query complexity is known.