Physical unclonable functions (PUFs) are widely considered in secret key generation for resource constrained devices. However, PUFs require additional hardware overhead. In this paper, we focus on developing a PUF-efficient, robust, and secure key generation scheme. First, a novel method for extracting quaternary PUF responses is proposed to increase the entropy of a PUF response, in which a 2-bit response is extracted from evaluating a single PUF cell multiple times. The probability masses of the responses can be adjusted by setting parameters appropriately. Then, a chosen secret model based fuzzy extractor (FE) is designed to extract secret keys from the quaternary PUF responses. To improve the security of this FE, it is modeled as a wiretap channel system, and wiretap polar coding is adopted to reduce secrecy leakage. An upper bound of secrecy leakage is also given in this paper, and it suggests that an arbitrarily small (even zero) leakage can be achieved by properly choosing parameters of the quaternary PUF responses generation. Comparison results show that the required number of PUF cells to achieve the same level of secrecy in our scheme is as low as half that of the state-of-the-art schemes.