Existing Side-Channel Attacks (SCAs) have several limitations and, rather than to be real attack methods, can only be considered to be security evaluation methods. Their limitations are mainly related to the sampling conditions, such as the trigger signal embedded in the source code of the encryption device, and the acquisition device that serves as the encryption-device controller. Apart from it being very difficult for an attacker to add a trigger into the original design before making an attack or to control the encryption device, there is a big gap in the capacity of existing SCAs to pose real threats to cipher devices. In this paper, we propose a new method, the sliding window SCA (SW-SCA), which can be applied in scenarios in which the acquisition device is independent of the encryption device and for which the encryption source code requires no trigger signal or modification. First, we describe the main issues in existing SCAs, then we theoretically analyze the effectiveness and complexity of our proposed SW-SCA -a method that can incorporate a sliding-window mechanism into almost all of the existing non-profiled SCAs. The experimental results for both simulated and physical traces verify the effectiveness of the SW-SCA and the appropriateness of its theoretical complexity.