  Observing the significance of spectrally-efficient secure non-orthogonal
multiple access (NOMA), this paper proposes a novel quality of service (QoS)
aware secure NOMA protocol that maximizes secrecy fairness among untrusted
users. Considering a base station (BS) and two users, a novel decoding order is
designed that provides security to both users. With the objective of ensuring
secrecy fairness between users, while satisfying their QoS requirements under
BS transmit power budget constraint, we explore the problem of minimizing the
maximum secrecy outage probability (SOP). Closed-form expression of pair outage
probability (POP) and optimal power allocation (PA) minimizing POP are
obtained. To analyze secrecy performance, analytical expressions of SOP for
both users are derived, and individual SOP minimization problems are solved
using concept of generalized-convexity. High signal-to-noise ratio
approximation of SOP and asymptotically optimized solution minimizing this
approximation is also found. Furthermore, a global-optimal solution from
secrecy fairness standpoint is obtained at low computational complexity, and
tight approximation is derived to get analytical insights. Numerical results
present useful insights on globally optimized PA which ensure secrecy fairness
and provide performance gain of about 55.12%, 69.30%, and 19.11%, respectively,
compared to fixed PA and individual users' optimal PAs. Finally, a tradeoff
between secrecy fairness performance and QoS demands is presented.
