In this paper, we propose a fully symmetrical obfuscated-interconnection PUF (SOI PUF), which contains n delay stages with each stage having 4k obfuscated interconnections for resisting machine learning (ML)-based modeling attacks. All the delay stages contribute to k PUF primitives while achieving a 20× increase in the number of possible interconnections with the same hardware resources over similar prior arts. The SOI PUF mathematical model also theoretically demonstrates the large number of nonlinear matrix multiplications for resisting ML-based modeling attacks. We further exploit parallel weak PUF cells and propose the challenge-obfuscated SOI PUF (cSOI PUF), which can effectively prevent adversaries from bypassing unknown interconnections through reverse engineering (RE) attacks. The proposed SOI PUF and cSOI PUFs are evaluated by both software simulation and FPGA measurements. Without requiring a large k as in the existing PUF architectures, the simulation results demonstrate that the proposed SOI and cSOI PUFs can achieve a ~50% prediction accuracy for k ≥ 3, even when facing ML attacks using 5-hidden-layer Artificial Neural Network (ANN) with 40M training CRPs. Furthermore, the proposed (64,2/4/6/8)-SOI PUF and (64,2/4/6/8)-cSOI PUF implemented using Xilinx Artix-7 FPGA can both achieve a measured reliability and uniformity of >94% and ~50%, respectively. Depending on the value of k, the uniqueness ranges from 29.1% to 42.7% for SOI PUFs, and further improves to ~50% for cSOI PUFs. The resilience against Reliability-based modeling attacks, Probably Approximately Correct (PAC) attacks and Reverse-Engineering-based modeling attacks will also be discussed.