Efficient Set Membership Encryption and Applications

The emerging area of laconic cryptography [Cho et al., CRYPTO'17] involves the design of two-party protocols involving a sender and a receiver, where the receiver's input is large. The key efficiency requirement is that the protocol communication complexity must be independent of the receiver's input size. In recent years, many tasks have been studied under this umbrella, including laconic oblivious transfer (lOT). In this work, we introduce the notion of Set Membership Encryption (SME) - a new member in the area of laconic cryptography. SME allows a sender to encrypt to one recipient from a universe of receivers, while using a small digest from a large subset of receivers. A recipient is only able to decrypt the message if and only if it is part of the large subset. We show that lOT can be derived from SME. We provide efficient constructions of SME using bilinear groups. Our solutions achieve orders of magnitude improvements in decryption times than state-of-the-art (on lOT) and significant improvements overall in concrete efficiency over initial works in the area of laconic cryptography, albeit at the cost of worse asymptotics.