This article addresses the privacy-preserving control issue for two-dimensional systems with probabilistic constraints. According to the exclusive or logical operation and the dynamic coding-decoding rule, a privacy-preserving mechanism (PPM) is developed, under which the transmitted data is efficiently compressed and encrypted into a ciphertext with finite bits. A PPM-based controller is designed that simultaneously guarantees a prescribed probabilistic constraint, mean-square boundedness, and privacy performance. Mathematical techniques, including mathematical induction, Chebyshev inequality, and matrix analysis, are employed to establish sufficient conditions for the presence of the desired controller gains. Additionally, the privacy and secrecy performance of the PPM is analyzed and simulation examples are presented to showcase the efficacy of the proposed controller design method.