The Physically Unclonable Function (PUF) is an emerging hardware security primitive that provides a promising solution for lightweight security. PUFs can be used to generate a secret key that depends on the manufacturing process variation for authentication and device identification. However, the resource requirements of PUFs pose challenges for their application in resource-constrained Internet of Things (IoT) devices. This work proposes a new approach for response extraction in Configurable Ring Oscillator (CRO) PUFs that contributes to reducing area and power consumption by eliminating the need for duplicating Ring Oscillators (ROs) and decreasing associated switching activity. The kernel-based response extraction approach exploits the phase shift of the delay elements and the frequency of ROs to generate unique responses effectively. The extraction approach uses a time-based kernel that enables the internal counters of the PUF and evaluates the propagated signals within ROs for a predefined period. The extraction approach has been implemented and verified on a design variant of the CRO PUF, which is also proposed within the scope of this work. The proposed PUF has been implemented in 22-nm FDSOI technology using Synopsys tools. A comprehensive security analysis has been conducted utilizing Challenge-Response Pairs (CRPs) collected from 8 chips. The extracted responses achieve an average of 49.42%, 38.25%, 9.95%, and 45.5% for uniformity, diffuseness, IntraHD, and uniqueness, respectively. Compared with state-of-the-art designs, the proposed design achieves an 86% reduction in area and a 65.1% reduction in power consumption while delivering 2