Ring Oscillator (RO) Physical Unclonable Function (PUF) is one of the most popular silicon PUFs which exploit manufacturing variations during the chip fabrication process. RO PUF can generate secret bits by comparing the frequency difference between two ROs. However, previous RO PUFs improve flexibility and reliability through adding redundant ROs and thus incur unacceptable hardware overheads. In this work, we propose a crossover RO PUF to improve flexibility and reliability and reduce hardware overheads. The basic idea is to implement one-to-one input-output mapping with Lookup Table (LUT)-based interstage crossing structure in each level of inverters. Experimental results show that our proposed structure has much lower hardware overheads and better uniqueness and reliability than the previous configurable RO PUFs. In addition, individual customization on configuration bits of interstage crossing structure and different RO selections by challenges bring high flexibility.