SMILE: Set Membership from Ideal Lattices with Applications to Ring Signatures and Confidential Transactions.

In a set membership proof, the public information consists of a set of elements and a commitment. The prover then produces a zero-knowledge proof showing that the commitment is indeed to some element from the set. This primitive is closely related to concepts like ring signatures and “one-out-of-many” proofs that underlie many anonymity and privacy protocols. The main result of this work is a new succinct lattice-based set membership proof whose size is logarithmic in the size of the set.