A new practical physical layer secret key generation in the presence of an untrusted relay

Physical layer secret key generation (SKG) has recently been introduced as a lightweight and efficient solution for sixth-generation (6G) networks. In this area, schemes based on local random generators are used for high-rate key generation. One of these schemes is random phase injection, where channel probe signals with random phases are exchanged between communication parties (source and destination). This paper proposes an SKG scheme in the presence of an untrusted relay, which helps the SKG process while cannot extract the secret key. To make the scheme operational, for the first time, the channel probe signals are considered discrete random phase based on M-PSK signals and a multi-bit quantizer is used in the reception. In addition, to reduce the key error rate, quantization with guard bands (GB) is used for key extraction. For such a scenario, we derive expressions for key agreement rate, key mismatch rate (KMR), key discarding rate (KDR) and key generation rate (KGR). Additionally, for the first time, this work examines the context of geometric secrecy for the proposed discrete phase key generation scheme for both direct and relaying scenarios. Through simulations, several engineering insights are presented to enhance the quality of the proposed SKG and its security.