Non-orthogonal multiple access (NOMA) and massive multiple-input multiple-output (MIMO) systems are highly efficient. Massive MIMO systems are inherently resistant to passive attackers (eavesdroppers), thanks to transmissions directed to the desired users. However, active attackers can transmit a combination of legitimate user pilot signals during the channel estimation phase. This way they can mislead the base station (BS) to rotate the transmission in their direction, and allow them to eavesdrop during the downlink data transmission phase. In this paper, we analyse this vulnerability in an improved system model and stronger adversary assumptions, and investigate how physical layer security can mitigate such attacks and ensure secure (confidential) communication. We derive the secrecy outage probability (SOP) and a lower bound on the ergodic secrecy capacity, using stochastic geometry tools when the number of antennas in the BSs tends to infinity. We adapt the result to evaluate the secrecy performance in massive orthogonal multiple access (OMA). We find that appropriate power allocation allows NOMA to outperform OMA in terms of ergodic secrecy rate and SOP.