Classical-quantum arbitrarily varying wiretap channel: Secret message transmission under jamming attacks

Abstract

We analyze arbitrarily varying classical-quantum wiretap channels. These channels are subject to two attacks at the same time: one passive (eavesdropping), and one active (jamming). We progress on previous works [11] and [12], by introducing a reduced class of allowed codes that fulfills a more stringent secrecy requirement than earlier definitions. In addition, we prove that non-symmetrizability of the legal link is sufficient for equality of the deterministic and the common randomness assisted secrecy capacities. At last, we focus on analytic properties of both secrecy capacities: We completely characterize their discontinuity points, and their super-activation properties.

Message Transmission over Classical Quantum Channels with a Jammer with Side Information, Correlation as Resource and Common Randomness Generating

“…Notice, the property (18) of the assignments to the 3 groups yields (17). Then next we shall show (16), by assume a contradiction, that (16)…”

“…. Our proof is based on constructions of two functions g 0 : V ι → X and g 1 : V ι → X (for a properly defined ι in the next paragraph), satisfying (16) and…”

“…When the jammer knew the shared randomness, he would render the shared randomness completely useless (cf. [16]). Thus we have to show that we can archive that the jammer, knowing the code word, has no access to the randomness.…”

“…In 1985 a necessary condition for this has been delivered in [22], and in 1988 [20] proved that this condition is also sufficient. In [16] it has been shown that the resource must be only known by the legal channel users, since otherwise it will be completely useless.…”

Message Transmission Over Classical Quantum Channels With a Jammer With Side Information: Message Transmission Capacity and Resources

“…The legal channel users' knowledge about the shared randomness is very helpful for message transmission through an arbitrarily varying channel (random correlated capacity), where we assume that the resource is only known by the legal channel users, since otherwise it will be completely useless (cf. [12]).…”