In this work we present sub-space modeling of strong PUF as a cost efficient solution for PUF enrollment for the designers' community. Our goal is to demonstrate a method which can reduce the overall cost in terms of number of CRPs required for training, training time and memory. Instead of modifying the estimated model structure, we propose to reduce the complexity of the modeling target. This means to provide secured access to the internal responses of strong PUF during the enrollment and capture internal CRPs to model each sub-component of the PUF independently. It also necessitates to permanently remove the internal access after the enrollment to prevent exposure of the internal responses. This means that the internal responses should not be directly accessible after enrollment. Our sub-space modeling method requires lesser number of CRPs compared to modeling the whole PUF. We experimentally prove that sub-space modeling can significantly reduce the cost of training compared to some of the latest works. For instance, we could model 128-stage 6-XOR Arbiter PUF with just above 90% prediction accuracy with 5000 CRPs. Here the response in the CRP is a vector including the responses of the sub-components. Our results show that sub-space modeling is potentially a cost-efficient solution to enroll strong PUF with high complexity.