On the using of Rényi’s quadratic entropy for physical layer key generation

Abstract

As a promising way for establishing secret keys, physical layer key generation has been broadly studied, which typically extracts secret keys with wireless channel characteristics. The existing schemes proved that temporal channel variations, channel reciprocity and spatial de-correlation of wireless channel greatly affected the performance of physical layer key generation. In this paper, the application of collision entropy (Rényi’s quadratic entropy) for improving physical layer key generation is discussed. Specifically, after collecting sufficient channel measurements, a channel measurement evaluation mechanism based on collision entropy is implemented to determine the adequacy of these measurements. Consequently, some consecutive measurements with smaller collision entropies are dropped and the reserved measurements are applied as input of the following process. Based on the evaluation mechanism, an adaptive and efficient key generation scheme is proposed. The proposed scheme consists of five components: channel probing, the evaluation mechanism, the adaptive quantization, information reconciliation and privacy amplification. To validate this scheme, several experiments in real environments are conducted. Different from the existing schemes, the received signal strength (RSS) measurements derived by heterogeneous devices are used as channel measurements. The results show that: (1) compared with homogeneous devices, RSS sequences of heterogeneous devices have more discrepancies and these discrepancies make key generation more challenging; (2) the proposed evaluation mechanism can effectively reduce bit mismatch rate and enhance the efficiency of information reconciliation; (3) compared with other schemes, the proposed key generation scheme can efficiently generate shared secret keys between heterogeneous transceivers in real environments.