  Remarkably, it has been shown that in principle, security proofs for quantum
key-distribution (QKD) protocols can be independent of assumptions on the
devices used and even of the fact that the adversary is limited by quantum
theory. All that is required instead is the absence of any hidden information
flow between the laboratories, a condition that can be enforced either by
shielding or by space-time causality. All known schemes for such Causal Key
Distribution (CKD) that offer noise-tolerance (and, hence, must use privacy
amplification as a crucial step) require multiple devices carrying out
measurements in parallel on each end of the protocol, where the number of
devices grows with the desired level of security. We investigate the power of
the adversary for more practical schemes, where both parties each use a single
device carrying out measurements consecutively. We provide a novel construction
of attacks that is strictly more powerful than the best known attacks and has
the potential to decide the question whether such practical CKD schemes are
possible in the negative.
