One possible device authentication method is based on device fingerprints, such as software- or hardware-based unique characteristics. In this paper, we propose a fingerprinting technique based on passive externally measured information, i.e., current consumption from the electrical network. The key insight is that small hardware discrepancies naturally exist even between same-electrical-circuit devices, making it feasible to identify slight variations in the consumed current under steady-state conditions. An experimental database of current consumption signals of two similar groups containing 20 same-model computer displays was collected. The resulting signals were classified using various state-of-the-art time-series classification (TSC) methods. We successfully identified 40 similar (same-model) electrical devices with about 94% precision, while most errors were concentrated in confusion between a small number of devices. A simplified empirical wavelet transform (EWT) paired with a linear discriminant analysis (LDA) classifier was shown to be the recommended classification method.