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Physical layer secret key generation exploits the reciprocal channelrandomness for key generation and has proven to be an effective additionsecurity layer in wireless communications. However, static or scarcely randomchannels require artificially induced dynamics to improve the secrecyperformance, e.g., using intelligent reflecting surface (IRS). One keychallenge is that the induced random phase from IRS is also reflected in thedirection to eavesdroppers (Eve). This leakage enables Eve nodes to estimatethe legitimate channels and secret key via a globally known pilot sequence. Tomitigate the secret key leakage issue, we propose to exploit random matrixtheory to inform the design of a new physical layer secret key generation(PL-SKG) algorithm. We prove that, when sending appropriate random Gaussianmatrices, the singular values of Alice's and Bob's received signals follow asimilar probability distribution. Leveraging these common singular values, wepropose a random Gaussian matrix based PL-SKG (RGM PL-SKG), which avoids theusages of the globally known pilot and thereby prevents the aforementionedleakage issue. Our results show the following: (i) high noise resistance whichleads to superior secret key rate (SKR) improvement (up to 300%) in low SNRregime, and (ii) general improved SKR performance against multiple colludedEves. We believe our combination of random matrix theory and PL-SKG shows a newparadigm to secure the wireless communication channels.

Random Matrix based Physical Layer Secret Key Generation in Static Channels