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This article is concerned with the secure particle filtering problem for a class of discrete-time nonlinear cyber-physical systems with binary sensors in the presence of non-Gaussian noises and multiple malicious attacks. The multiple attacks launched by the adversaries, which take place in a random manner, include the denial-of-service attacks, the deception attacks, and the flipping attacks. Three sequences of Bernoulli-distributed random variables with known probability distributions are employed to describe the characteristics of the random occurrence of the multiple attacks. The raw or corrupted measurements are transmitted to sensors, whose outputs are binary according to engineering practice. A modified likelihood function is constructed to compensate for the influence of the randomly occurring multiple attacks by introducing the random occurrence probability information into the design process. Subsequently, a secure particle filter is proposed based on the constructed likelihood function. Finally, a moving target tracking application is elaborated to verify the viability of the proposed secure particle filtering algorithm.