Secret Keys from Dirty Paper Coding Clause Samples
Secret Keys from Dirty Paper Coding. We study the Gaussian case under an average power constraint. The channel to the legitimate receiver and the eavesdropper is expressed as: where the maximization is over all auxilary random variables u that obey the Markov chain u (x, s) (yr, ye). Additionally it suffices to limit the cardinality of the auxiliary variable to (1 + ) in (18). → → |S| |X | The achievability in (18) follows from (7) by augmenting yr = x + s + zr
Secret Keys from Dirty Paper Coding. We study the Gaussian case under an average power lim P →∞ lim Q→∞ 2 R+ − R− = 0 (16) R+ − R− = 0 (17) constraint. The channel to the legitimate receiver and the eavesdropper is expressed as: yr = x + s + zr (11) ye = x + s + ze, 1Interestingly in the presence of public discussion, we have been able to characterize the secret-key capacity [1]. 2The constraint P ≥ 1 guarantees that (13) has a solution in ρ. More generally lower bound is also valid for all values of P and Q for which (13) has a solution in ρ however the constraint P ≥ 1 suffices to obtain the optimality results in Prop. 4. Upper Bound Lower Bound Capacity with Public Discussion Secret Message Lower Bound Upper Bound Capacity with Discussion Lower Bound Secret−Message Transmission