Research On Secret Key Generation Rate For Physical Layer Security Model

With the increase of terminal computing power and the development of quantum computers,the secret keys in the upper layer of the protocol stack cryptography based on computational complexity are at risk of being cracked.The 5th generation(5G)mobile communication network’s deployment intensification and the demand for massive access add difficulties to the update and management of secret keys.The physical layer secret key generation technology,from an information-theoretic perspective,provides a way to generate "absolutely secure" secret keys independent of computational complexity,and the inherent randomness and time-varying nature of wireless physical layer channels provide rich resources for secret key updating,which can complement cryptographic security mechanisms.The performance of physical layer secret key generation is mainly measured by the secret key generation rate,and its research is oriented to two type of models:the physical layer security theoretical model and the physical layer channel characteristics model.The study of the physical layer security theoretical model can provide performance limits for the actual physical layer secret key generation protocol;the study of the physical layer channel characteristics model can provide the theoretical basis for parameter selection for the engineering implementation of physical layer secret key generation.In this dissertation,the research on physical layer secret key generation rate will be carried out separately for the two models,focusing on the derivation of the secret key generation rate and the factors affecting the secret key generation rate.The main research results are as follows.(1)Analysis of group key-private key generation rate region based on trusted terminal collaboration.For the source model in the theoretical model of physical layer security,the group key-private key generation rate region of the three-terminal model is considered to be enhanced by introducing a trusted collaborative terminal.The secret key generation region of the group key-private key is derived based on the cut-set theory;the inverse proof of the rate region is carried out based on Feno’s inequality and the basic definition of mutual information;the secret key generation rate region of group key-private key is analyzed for different source distributions,and for each case,the achievability of the derived rate region of group key-private key is proved based on double random binning and joint typicality decoding methods;the security of group key-private key is proved by analyzing the key leakage rate;and the rate region is further extended to the scenario of Gaussian correlated sources;Examples are also given to illustrate the theoretical guidance of the study of this model for the physical layer channel characteristics model.The multi-key generation rate region explored in this study can be used as a theoretical limit for physical layer multi-key generation in wireless collaborative communication networks.(2)Analysis of private key and group key generation rate regions based on the joint source-channel model.For the joint source-channel model in the physical layer security theoretical model,the same types of secret keys as in the first study are considered to be generated,using both the wiretap broadcast channel and the correlated source,i.e.,a private key for the single receiverdouble eavesdropping scenario and a group key for the double-receiver-single eavesdropping scenario.Based on the security conditions of the secret key,the secret key generation rate regions of the private key and group key are derived;the inverse and the achievability of the rate regions are proved based on Feno’s inequality and the basic definition of mutual information,using the double random binning and joint typicality decoding methods;the security of private key and group key is proved by analyzing the key leakage rate;further extending the rate region to the scenarios of Gaussian channels and Gaussian sources.The private key and group key generation rate regions explored in this study can be used as the theoretical limits for secret key generation in the physical layer wiretap broadcast channel.(3)Secret key generation rate analysis of collaborative networks based on physical layer channel characteristics.For the collaboration-based physical layer channel characteristics model,four random source extraction schemes for full-duplex(FD)amplify-and-forward(AF)relay networks are designed,and the closed-form expressions for the secret key generation rate under Rayleigh fading channels are derived;for the double intelligent reflecting surface(IRS)model with the spatial correlation of reflecting elements,the closed-form expression for the secret key generation rate in Rayleigh fading channel is derived.The simulation results show that the secret key generation rate is inversely proportional to the residual self-interference(RSI)under the FD-AF relay network;the spatial correlation is a favorable factor for the equal phase configuration and a degenerate factor for the random phase configuration under the IRS network;the distributed IRS system can achieve 21%higher secret key generation rate gain than deploying all reflecting elements on one IRS.The model targeted in this study is a special scenario of the first research model,which can provide a theoretical basis for the selection of parameters for secret key generation,in wireless collaborative communication networks.(4)Secret key generation rate analysis based on correlated Nakagamim fading channel.For the secret key generation model with correlated eavesdropping channel,the secret key generation rate under the Nakagami-m wireless fading channel is derived;the expressions of autocorrelation and crosscorrelation in power terms are derived for m values as integers.The simulation results show that the secret key generation rate is proportional to the value of the m fading parameter,and it follows that the secret key generation rate when the received signal envelope obeys the Rice distribution(m>1)is higher than that of the Rayleigh distribution(m=1).Since the Nakagami-m distribution can be equated to different common distributions,by setting different values of the fading parameter m,the secret key generation rate expression obtained in this study is a general form.