<p>This paper proposes a piecewise Burgers’ map (PBM) generated by replacing the quadratic nonlinearity of the Burgers’ map with an absolute value function. It involves dynamical probing, microcontroller execution, derivation of random number generation (RNG), and secure steganography application with two-level chaos-based encryption on a PBM. PBM has trivial, line, or symmetric fixed points depending on its parameters. Stability analysis of the fixed points results in stable and unstable fixed points in the considered plane. The numerical simulations of PBM reveal limit cycles, quasiperiodic characteristics, a quasiperiodic route to chaos, and five different shapes of chaotic characteristics. Two constant parameters are introduced in the rate equations of PBM to implement partial and total amplitude controls. The dynamical behaviors of PBM are validated by the design of the microcontroller implementation. An RNG based on PBM is developed for the process of secure steganography application with two-level chaos-based encryption. The generated bit sequences validate the NIST 800 − 22 tests. A chaos-based Blowfish algorithm is proposed using this RNG, and the image is encrypted. In the proposed image privacy algorithm, first a random 64-bit key and initialization vector (IV) are generated from PBM sequences. The input image is permuted with these sequences and then encrypted using the Blowfish algorithm in CBC mode. Subsequently, PBM-generated random numbers are used to select cover pixels, and the encrypted bits are embedded through a 4-LSB substitution strategy. This procedure is repeated for the entire binary data of the original image to construct the final steganographic image. The encryption and data hiding processes are checked for their security performances, and their performances are evaluated. The proposed method has high performance and provides superior protection against statistical analysis attacks, as shown by the results.</p>