In this paper, we consider a cooperative cognitive radio non-orthogonal multiple access network, where a secondary transmitter (ST) assists transmission of a primary source-destination (PS-PD) pair, while simultaneously communicating with a secondary receiver. Specifically, ST acts as an untrusted relay for primary network, that overhears the primary confidential messages. To improve the secrecy of the network, we consider a secure transmission with friendly jamming, in which a friendly jammer transmits a jamming signal to confound the untrusted relay and accordingly to increase the secrecy performance of the primary network. We derive closed-form expressions for the secrecy outage probability, intercept probability, and average secrecy rate. Moreover, an optimal power allocation scheme between the PS and jammer is developed to maximize the instantaneous secrecy rate of the primary network, while ensuring an specific QoS for secondary network. Our findings reveal that proposed scheme can significantly enhance the secrecy of the system, especially when the quality of PS-ST link is inferior to that of the jammer-ST link. In particular, at high signal-to-noise ratio regime, optimal power allocation achieves the average secrecy rate of 0.72 bps/Hz, which is about 2.25 times than that of equal power allocation. (C) 2020 Elsevier GmbH. All rights reserved.