Reversible data hiding (RDH) techniques recover the original cover image after data extraction. Thus, they have gained popularity in e-healthcare, law forensics, and military applications. However, histogram shifting using a reversible data embedding technique suffers from low embedding capacity and high variability. This work proposes a technique in which the distribution obtained from the cover image determines the pixels that attain a peak or zero distribution. Afterward, adjacent histogram bins of the peak point are shifted, and data embedding is performed using the least significant bit (LSB) technique in the peak pixels. Furthermore, the robustness and embedding capacity are improved using the proposed dynamic block-wise reversible embedding strategy. Besides, the secret data are encrypted before embedding to further strengthen security. The experimental evaluation suggests that the proposed work attains superior stego images with a peak signal-to-noise ratio (PSNR) of more than 58 dB for 0.9 bits per pixel (BPP). Additionally, the results of the two-sample t-test and the Kolmogorov–Smirnov test reveal that the proposed work is resistant to attacks.