We show how a polynomial-time prover can commit to an arbitrary finite set Ë of strings so that, later on, he can, for any string Ü, reveal with a proof whether Ü ¾ Ë or Ü ...
We introduce the notion of non-malleable noninteractive zero-knowledge (NIZK) proof systems. We show how to transform any ordinary NIZK proof system into one that has strong non-m...
Zero knowledge sets (ZKS) [18] allow a party to commit to a secret set S and then to, non interactively, produce proofs for statements such as x ∈ S or x /∈ S. As recognized in...
Let Λ : {0, 1}n ×{0, 1}m → {0, 1} be a Boolean formula of size d, or more generally, an arithmetic circuit of degree d, known to both Alice and Bob, and let y ∈ {0, 1}m be a...
We show that probabilistically checkable proofs can be used to shorten non-interactive zero-knowledge proofs. We obtain publicly verifiable non-interactive zero-knowledge proofs fo...