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 server of banks, hospitals, that providing 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 bluevia entanglement swapping between two hackers can cause uncontrolled consumption of resources. Turning into positive a recently proven no-go result by M. Christandl et al.  we propose a natural countermeasure to 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 memory overhead. In particular, we show that to avoid possibility of entanglement swapping, it is necessary to store at least twice as much of 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 twoway repeater rate for states with positive partial transposition (PPT), which approximates strictly irreducible private states. As a byproduct, we provide a lower bound on trace distance between PPT and private states, shown previously only for private bits.