In this paper, we investigate non-orthogonal multiple access (NOMA) assisted secure computation offloading under the eavesdropping-attack, in which a malicious node overhears the edge-computing user's (EU's) offloading transmission to the edge-computing server (ES), and NOMA is used for the EU's offloading and meanwhile for providing artificial jamming to the eavesdropper. Since multi-user simultaneous transmission over a same frequency channel can be enabled by NOMA, a wireless user (WU) can form a NOMA pair with the EU to provide cooperative jamming to the eavesdropper while also gaining an opportunity of sending its data. Focusing on the EU-WU pair with the fixed WU's energy-provisioning, we exploit the physical layer security to quantify the EU's offloading throughput with the help of WU's jamming. We then study the joint optimization of the EU's computation offloading and the EU-WU's NOMA transmission for minimizing the EU's total energy consumption subject to its latency-requirement in completing the computation-task. By utilizing the feature of analytical solution of the WU's transmission, we then investigate the WU's optimal energy-provisioning for the EU-WU pair, such that both the EU and WU can benefit from the cooperative jamming in a fairness manner. Specifically, we formulate the EU-WU's cooperation as a Nash bargaining game. By identifying the monotonic feature of Nash bargaining problem, we propose a polyblock approximation based algorithm for determining the WU's optimal energy-provisioning to achieve the win-win solution for the paired EU and WU. Finally, we investigate the scenario of multiple EUs and WUs, and aim at finding the stable pairing between the EUs and WUs, such that no individual EU (or WU) would like to change its partner. An efficient algorithm, which is based on the Gale-Shapley theory while exploiting the quantitative feature of EUs' and WUs' net-rewards, is proposed to achieve the stable EU-WU pairings. Numerical results are provided to validate our proposed algorithms and demonstrate the advantage of our proposed NOMA assisted computation offloading via cooperative jamming.