In this paper, we study the design of secure communication for time division duplexing multi-cell multi-user massive multiple-input multiple-output (MIMO) systems with active eavesdropping. We assume that the eavesdropper actively attacks the uplink pilot transmission and the uplink data transmission before eavesdropping the downlink data transmission phase of the desired users. We exploit both the received pilots and data signals for uplink channel estimation. We show analytically that when the number of transmit antennas and the length of the data vector both tend to infinity, the signals of the desired user and the eavesdropper lie in different eigenspaces of the received signal matrix at the base station if their signal powers are different. This finding reveals that decreasing (instead of increasing) the desire user's signal power might be an effective approach to combat a strong active attack from an eavesdropper. Inspired by this result, we propose a data-aided secure downlink transmission scheme and derive an asymptotic achievable secrecy sum-rate expression for the proposed design. Numerical results indicate that under strong active attacks, the proposed design achieves significant secrecy rate gains compared to the conventional design employing matched filter precoding and artificial noise generation.