Key Exchange for Two-Way Untrusted Relaying Systems Through Constellation Overlapping

This letter proposes a key exchange scheme for the untrusted relay system, where the relay not only assists in message transmission but also tries to recover messages. Terminal users initiate the process by transmitting a local key and utilize constellation overlapping techniques to create an overlapped constellation at the relay nodes, which increases the decoding error rate for relay eavesdropping but still poses a risk of key leakage. To address this, we propose a fine-grained entropy extraction algorithm that quantifies the overlapped constellation points into key bits, which are uniformly random bits from the relay’s perspective. In the constellation overlapping scenario, we can estimate the number of instances where the relay cannot distinguish. Leveraging this, our algorithm achieves remarkable levels of entropy utilization. QPSK enables perfect lossless entropy extraction, while other QAM modulation schemes can achieve a utilization rate of up to 96%.