The secrecy performance of continuous-aperture array (CAPA)-based wiretap channels in terms of secrecy rate and secrecy outage probability (SOP) is analyzed. First, the system models of CAPA systems with maximum-ratio transmission under a Rayleigh fading channel are established, and approximate probability density functions for the legitimate user Bob's signal-to-noise ratio (SNR) and the eavesdropper Eve's SNR are derived using Mercer's theorem and Landau's eigenvalue theorem. Three scenarios are considered, including a single Eve, multiple independent Eves, and multiple collaborative Eves. Next, the expressions of the secrecy rate and SOP under these three scenarios are derived, and the high-SNR slope, high-SNR power offset, diversity order, and array gain in Bob's high-SNR region are obtained. It is then theoretically proven that, in all three scenarios, the CAPA system achieves the same high-SNR slope and the same diversity order, with the latter being equal to the spatial degrees of freedom. Moreover, the CAPA system with a single Eve has the smallest high-SNR offset and the highest array gain, whereas the CAPA system with multiple collaborative Eves exhibits the largest high-SNR offset and the lowest array gain. Finally, the theoretical analyses of secrecy rate, SOP, high-SNR performance are validated by the simulation results, and a higher secrecy rate and a lower SOP are achieved by the CAPA systems compared to the spatially-discrete array systems with half-wavelength antenna spacing.