This paper investigates the employment of photoplethysmography (PPG) for user authentication systems. Time-stable and user-specific features are developed by stretching the signal, designing a convolutional neural network and performing a variation-stable approach with three score fusions. Two evaluation scenarios are explored, namely single-session and two-sessions. In the earlier, the training and testing are done solely on one session data to find the user-specific features, while the second scenario is performed on data from two different sessions to test the time permanence of the features. The verification system was tested on four databases achieving an accuracy of 100% for single-session and 87.3% for two-sessions cases. The simulation results confirm the effectiveness of proposed variation-stable fusion which can be extended to other biometrics.