Introduction to Cryptographic Protocols

1 : x||y String x is concatenated with string y. 2 : λ(C) Distribution of a given instance or random variable C. 3 : D(X, Y) Statistical distance between the distributions of the two random variables X and Y. 6 : = Stat Statistical indistinguishability between two Random Variables: see Definition 8. 7 : = Comp Computational indistinguishability between two Random Variables: see Definition 9. 8 : Protocol proving equality between two bit commitments: b 0 b 1 , the commitment protocol is implied by the flavor of the commitments used. 9 : ↔ When commitment a is unveiled, it is accepted by the receiver as a valid commitment to the value b : a ↔ b. 10 : U (·) The operator U is a shorthand notation representing all the info necessary to unveil a given value: U (a) is all the information necessary such that the receiver can verify that a ↔ a. 11 : U n Uniform random variable over a set of n elements or 2 n elements, the meaning will be clear from the context. 12 : Pr[A(x) = y] Probability that probabilistic algorithm A outputs y given x. 13 : Pr x [A(x) = y] Average probability, over all x that probabilistic algorithm A outputs y given x : Pr x [A(x) = y] = x p x Pr[A(x) = y]. 1 : Statistical Distance Let X and Y be two random variables over the same set {x} x , then D(X, Y) =