Secret Keys from Dirty Paper Coding Sample Clauses

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 1.8 1.2 1.6 1 1.4 Rate 1.2 0.8 Rate 0.6 0.6 0.4 0.4 0.2 0.2 0 0 5 10 15 SNR (dB) 0 ∆ (dB)

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