In this paper, a secure communication model for cognitive multi-user massive multiple-input multiple-output (MIMO) systems with underlay spectrum sharing is investigated. A secondary (cognitive) multi-user massive MIMO system is underlaid within a primary (licensed) multi-user massive MIMO system. A passive multi-antenna eavesdropper is eavesdropping upon either the primary or secondary transmission. To this end, physical layer secure transmissions are provisioned for both primary and secondary systems by exploiting linear precoders and artificial noise (AN) generation. The excess degrees-of-freedom at the primary massive MIMO base-station are exploited to transmit the AN sequence by using random AN shaping matrices for the purpose of degrading the signal decodability at the eavesdropper. Achievable asymptotic secrecy rates for infinitely many base-station antennas are derived, and these secrecy rates are shown to be independent of the eavesdropper channels. Moreover, for infinitely many secondary base-station antennas, the secondary system becomes independent of the primary system allowing it to operate at its maximum transmission power without disturbing the primary system.