Evolving Conditional Disclosure of Secrets

In this work, we define and study the notion of evolving conditional disclosure of secrets (CDS) protocols. In this model, parties arrive infinitely in sequential order. Each party holds a private input, and when arrives, it sends a random message to a referee. In turn, at any stage of the protocol, the referee should be able to reconstruct a secret string, held by all the parties, from the messages it gets, if and only if the inputs of the parties that arrived satisfy some condition. A similar notion was previously presented for secret sharing, a closely related cryptographic primitive used in many secure protocols. In a secret sharing scheme, a dealer holds a secret string. It randomly generates shares and distributes them to a set of parties, one share for each party, such that only some predefined subsets of the parties would be able to reconstruct the secret from their shares. In addition to the initiation of evolving CDS, we present a few constructions of evolving CDS protocols, for different classes of conditions that should be satisfied by the inputs of the parties. We believe that our new notion can be used to better understand evolving secret sharing and other related cryptographic primitives, and that further applications and constructions of it will be found in the future.