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The security of quantum key distribution (QKD) can easily be obscured if the eavesdropper can utilize technical imperfections of the actual implementation. Here we describe and experimentally demonstrate a very simple but highly effective attack which even does not need to intercept the quantum channel at all. Only by exploiting the dead time effect of single photon detectors the eavesdropper is able to gain (asymptotically) full information about the generated keys without being detected by state-of-the-art QKD protocols. In our experiment, the eavesdropper inferred up to 98.8% of the key correctly, without increasing the bit error rate between Alice and Bob significantly. Yet, we find an evenly simple and effective countermeasure to inhibit this and similar attacks.