In this work, we consider two very natural extensions of secret sharing. In the first, which we call distributed} secret sharing, there is no trusted dealer at all, and instead the role of the dealer is distributed amongst the parties themselves. Distributed secret sharing can be thought of as combining the features of multiparty non-interactive key exchange and standard secret sharing, and may be useful in settings where the secret is so sensitive that no one individual dealer can be trusted with the secret. Our second notion is called functional secret sharing, which incorporates some of the features of functional encryption into secret sharing by providing more fine-grained access to the secret. Qualified subsets of parties do not learn the secret, but instead learn some function applied to the secret, with each set of parties potentially learning a different function.
Our main result is that both of the extensions above are equivalent to several recent cutting-edge primitives. In particular, general-purpose distributed secret sharing is equivalent to witness PRFs, and general-purpose functional secret sharing is equivalent to indistinguishability obfuscation. Thus, our work shows that it is possible to view some of the recent developments in cryptography through a secret sharing lens, yielding new insights about both these cutting-edge primitives and secret sharing.Category / Keywords: foundations / secret sharing Original Publication (in the same form): IACR-TCC-2016 Date: received 22 Jul 2015, last revised 21 Oct 2015 Contact author: ilan komargodski at weizmann ac il Available format(s): PDF | BibTeX Citation Version: 20151021:061842 (All versions of this report) Short URL: ia.cr/2015/735 Discussion forum: Show discussion | Start new discussion