  A significant number of servers that constitute the Internet are to provide
private data via private communication channels to mutually anonymous
registered users. Such are the servers of banks, hospitals that provide cloud
storage and many others. Replacing communication channels by maximally
entangled states is a promising idea for the quantum-secured Internet (QI).
While it is an important idea for large distances secure communication, for the
case of the mentioned class of servers pure entanglement based solution is not
only unnecessary but also opens a threat. A crack stimulating a node to
generate secure connections via entanglement swapping between two hackers can
cause uncontrolled consumption of resources. Turning into positive a recently
proven no-go result by S. B\"auml et al. [15], we propose a natural
countermeasure against this threat. The solution bases on connections between
hub-nodes and end-users realized with states that contain secure key but do not
allow for swapping of this key.We then focus on the study of the quantum memory
cost of such a scheme and prove a fundamental lower bound on its memory
overhead. In particular, we show that to avoid the possibility of entanglement
swapping, it is necessary to store at least twice as much memory than it is the
case in standard quantum-repeater-based network design. For schemes employing
either states with positive partial transposition that approximates certain
privates states or private states hardly distinguishable from their attacked
versions, we derive much tighter lower bounds on required memory. Our
considerations yield upper bounds on a two-way repeater rate for states with
positive partial transposition (PPT), which approximates strictly irreducible
private states. As a byproduct, we provide a lower bound on the trace distance
between PPT and private states, shown previously only for private bits.
