Non-Interactive Verifiable Secret Sharing for Monotone Circuits

We propose a computationally secure and non-interactive verifiable secret sharing scheme that can be efficiently constructed from any monotone Boolean circuit. By non-interactive we mean that the dealer needs to be active only once, where he posts a public message as well as a private message to each shareholder. In the random oracle model, we can even avoid interaction between shareholders. By efficient, we mean that we avoid generic zero-knowledge techniques. Such efficient constructions were previously only known from linear secret sharing schemes (LSSS). It is believed that the class of access structures that can be handled with polynomial size LSSS is incomparable to the class that can be recognized by polynomial size monotone circuits, so in this sense we extend the class of access structures with efficient and non-interactive VSS.