Unconditional Secrecy and Computational Complexity against Wireless Eavesdropping

Unconditional secrecy (UNS) of a wireless transmission scheme refers to the minimum amount of secrecy of the scheme subject to eavesdropping by eavesdropper (Eve) with any number of antennas and any noise level. For each coherence period of wireless channels, the UNS achievable is known to be limited by the entropy of user’s reciprocal channel state information (subject to a proper level of quantization). While UNS rate may be too limited for environment with low mobility, it is possible to design physical layer encryption methods to increase the computational complexities that Eve has to overcome in order to break further secrecy beyond UNS. In this paper, we quantify the UNS of several classic transmission schemes and examine the complexity needed to break further secrecy beyond UNS of these schemes. We also provide a UNS and complexity analysis of a recently proposed physical layer encryption scheme called randomized reciprocal channel modulation (RRCM), and show an example where the complexity may exceed Eve’s capability.