Common use of Wolf Clause in Contracts

Wolf. 64]) Suppose that ▇▇▇▇▇, ▇▇▇, and ▇▇▇ get X = (X1, X2, . . . , Xn), Y = (Y1, Y2, . . . , Yn), resp. Z = (Z1, Z2, . . . , Zn) during the initialization phase. Let PXY Z = Qn PX Y Z . We use X, Y, and Z to represent Xi, Yi, and Zi, since the joint probability distributions of Xi, Yi, and Zi are the same for i = 1, 2, . . . , n. The secret-key rate of X and Y with respect to Z, denoted by S(X; Y Z), is defined as the largest nonnegative real number R such that for every ϵ > 0 and sufficiently large n = n(ϵ), there exists a (PXY Z, (R ϵ)n, ϵ) protocol for secret key agreement. More precisely, ▇▇▇▇▇ and ▇▇▇ get SA and SB respectively, which satisfy H(SA)/n ≥ R − ϵ, Pr [SA /= SB] ≤ ϵ, I(SA; ZW ) ≤ ϵ, H(SA) ≥ log |SA| − ϵ. (Recall that W denotes the public information during the communication phase) It is easy to see that S(X; Y ||Z) is related to PXY Z. In [43], the following upper bound and lower bound for S(X; Y ||Z) were proved: S(X; Y ||Z) ≤ min{I(X; Y ), I(X; Y |Z)}, (1.1)