Robustness of Physical Layer Security Primitives Against Attacks on Pseudorandom Generators

Physical layer security protocols exploit inviolable physical laws at the signal level for providing guarantees on secrecy of communications. These protocols invariably involve randomized encoding at the transmitter, for which an ideal random number generator is typically assumed in the literature. In this work, we study the impact of using weak Pseudo Random Number Generators (PRNGs) in physical layer security protocols for coding and forward key distribution over Binary Symmetric and Gaussian wiretap channels. In the case of wiretap channel coding, we study fast correlation attacks that aim to retrieve the initial seed used in the PRNGs. Our results show that randomized coset encoding, which forms an important part of wiretap channel coding, provides useful robustness against fast correlation attacks. In the case of single-round or forward key distribution over a Gaussian wiretap channel, the bits from a PRNG are nonlinearly transformed to generate Gaussian-distributed pseudo random numbers at the transmitter. In such cases, we design modified versions of the fast correlation attacks accounting for the effects of the nonlinear transformation and soft input. We observe that, even for moderately high memory, the success probability of the modified fast correlation attacks become the same as that of a random guess in many cases.