an:06987967
Zbl 1429.94061
Komargodski, Ilan; Zhandry, Mark
Cutting-edge cryptography through the lens of secret sharing
EN
Inf. Comput. 263, 75-96 (2018).
00423601
2018
j
94A60 94A62
computational secret sharing; witness PRFs; indistinguishability obfuscation
Summary: Secret sharing is a mechanism by which a trusted dealer holding a secret ``splits'' the secret into many ``shares'' and distributes the shares to a collection of parties. Associated with the sharing is a monotone access structure, that specifies which parties are ``qualified'' and which are not: any qualified subset of parties can (efficiently) reconstruct the secret, but no unqualified subset can learn anything about the secret. In the most general form of secret sharing, the access structure can be any monotone \textsf{NP} language.
In this work, we consider two very natural extensions of secret sharing. In the first, which we call \textit{distributed} secret sharing, there is no trusted dealer at all, and it can be thought of as combining the features of multiparty non-interactive key exchange and standard secret sharing. Qualified sets can agree on a key which remains pseudorandom for unqualified sets. Our second notion is called \textit{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 \textit{different} function.
Our main result is that both of the extensions above are \textit{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.