  Physical layer key generation (PLKG) can significantly enhance the security
of classic encryption schemes by enabling them to change their secret keys
significantly faster and more efficient. However, due to the reliance of PLKG
techniques on channel medium, reaching a high secret key rate is challenging in
static environments. Recently, exploiting intelligent reflecting surface (IRS)
as a means to induce randomness in static wireless channels has received
significant research interest. However, the impact of spatial correlation
between the IRS elements is rarely studied. To be specific, for the first time,
in this contribution, we take into account a spatially correlated IRS which
intends to enhance the secret key generation (SKG) rate in a static medium.
Closed form analytical expressions for SKG rate are derived for the two cases
of random phase shift and equal random phase shift for all the IRS elements. We
also analyze the temporal correlation between the channel samples to ensure the
randomness of the generated secret key sequence. We further formulate an
optimization problem in which we determine the optimal portion of time within a
coherence interval dedicated for the direct and indirect channel estimation. We
show the accuracy and the fast convergence of our proposed sequential convex
programming (SCP) based algorithm and discuss the various parameters affecting
spatially correlated IRS assisted PLKG.
