Physical unclonable functions (PUFs) are efficient primitives to generate authentication signatures and security keys. However, PUFs may be sensitive to noise and environmental conditions inducing reliability issues. Digital PUFs (DPUFs), which are by design inherently robust, have recently been proposed in the literature. They rely on static source of entropy: random structures produced by specific manufacturing process. In this paper, we propose secure efficient circuits to extract responses from these structures and further develop strong DPUF model. We first review the existing DPUF fabrication processes and associate extraction circuits, and discuss possible optimization in terms of cost and security. We notably use substitution–permutation networks (SPN) as a logical scheme to extract the DPUF data. The SPN circuit performances depend not only on network parameters but also by dimension and randomness of DPUF structures. We modelize and evaluate diverse SPN circuit settings providing ideal configurations for security-cost trade-off. Finally, we measure the implementation cost, identifying the most optimized configuration which reduces the circuit area. Our final SPN circuit for strong DPUF model needs less than 12,000 $${um}^{2}$$ circuit area (for a 45 nm technology node) and diffuseness is estimated to 0.5 ± 0.001. The results make SPN-based strong DPUF a pertinent alternative to classic PUF.