  Physical layer secret key generation exploits the reciprocal channel
randomness for key generation and has proven to be an effective addition
security layer in wireless communications. However, static or scarcely random
channels require artificially induced dynamics to improve the secrecy
performance, e.g., using intelligent reflecting surface (IRS). One key
challenge is that the induced random phase from IRS is also reflected in the
direction to eavesdroppers (Eve). This leakage enables Eve nodes to estimate
the legitimate channels and secret key via a globally known pilot sequence. To
mitigate the secret key leakage issue, we propose to exploit random matrix
theory to inform the design of a new physical layer secret key generation
(PL-SKG) algorithm. We prove that, when sending appropriate random Gaussian
matrices, the singular values of Alice's and Bob's received signals follow a
similar probability distribution. Leveraging these common singular values, we
propose a random Gaussian matrix based PL-SKG (RGM PL-SKG), which avoids the
usages of the globally known pilot and thereby prevents the aforementioned
leakage issue. Our results show the following: (i) high noise resistance which
leads to superior secret key rate (SKR) improvement (up to 300%) in low SNR
regime, and (ii) general improved SKR performance against multiple colluded
Eves. We believe our combination of random matrix theory and PL-SKG shows a new
paradigm to secure the wireless communication channels.
