  The non-terrestrial networks (NTNs) are recognized as a key component to
provide cost-effective and high-capacity ubiquitous connectivity in the future
wireless communications. In this paper, we investigate the secure transmission
in a terahertz (THz)-empowered reconfigurable intelligent surface
(RIS)-assisted NTN (T-RANTN), which is composed of a low-Earth orbit satellite
transmitter, an RIS-installed high-altitude platform (HAP) and two unmanned
aerial vehicle (UAV) receivers, only one of which is trustworthy. An
approximate ergodic secrecy rate (ESR) expression is derived when the
atmosphere turbulence and pointing error due to the characteristics of THz as
well as the phase errors resulting from finite precision of RIS and imperfect
channel estimation are taken into account simultaneously. Furthermore,
according to the statistical and perfect channel state information of the
untrustworthy receiver, we optimize the phase shifts of RIS to maximize the
lower bound of secrecy rate (SR) and instantaneous SR, respectively, by using
semidefinite relaxation method. Simulation results show that both the
approximate expression for the ESR and the optimization algorithms are
serviceable, and even when the jitter standard variance of the trustworthy
receiver is greater than that of the untrustworthy one, a positive SR can still
be guaranteed.
