Lecture 10 : Zero Knowledge Proofs ( II )

Definition 1 (Zero-knowledge) An interactive proof (P,V) for a language L with witness relation R is said to be zero-knowledge if for every non-uniform PPT adversary V∗, there exists a PPT simulator S such that for every non-uniform PPT distinguisher D, there exists a negligible function ν(·) such that for every x ∈ L,w ∈ R(x), z ∈ {0, 1}∗, D distinguishes between the following distributions with probability at most ν(|x|): { ViewV ∗ [P(x,w)↔ V∗(x, z)] } and { S(1, x, z) } .