עמוס ביימל

In this work we introduce and study threshold (t-out-of-n) secret sharing schemes for families of functions F. Such schemes allow any set of at least t parties to compute privately the value f(s) of a (previously distributed) secret s, for any f ∈ F. Smaller sets of players get no more information about the secret than what follows from the value f(s). The goal is to make the shares as short as possible. Results are obtained for two different settings: we study the case when the evaluation is done on a broadcast channel without interaction, and we examine what can be gained by allowing evaluations to be done interactively via private channels.