Adaptive Remainder Modulo m Data Hiding

A problem of irreversible data hiding (DH), producing stego images resistant to steganalysis, is considered in spatial domain of gray-scale cover images. Stego image detection error (DE) is maximized when data is hidden (embedded) into noisy-like image areas where pixel values vary significantly. It is proved herein that generalization of the well-known least-significant bit (LSB) substitution to remainder modulo m (RM-m) DH method has an embedding invariant preserved after DH. A new adaptive remainder modulo m (ARM-m) method hiding data first in maximal noisy blocks by RM-m is proposed. ARM-m uses the invariant to construct a block complexity measure for adaptation. Ensemble classifiers and subtractive pixel adjacency matrix (SPAM) with 686 features were used to evaluate stego image DE on 886 images from UCID v.2 database. Compared to the state-of-the-art methods, ARM-4 with 2x2 blocks has DE=41.86% versus 24.42% of the best known method for 1 bit per pixel (bpp) embedding rate (ER). For ER=1.33 bpp, not reachable for known adaptive methods, ARM-4 and ARM-16, both with 8x8 blocks, have DE=27.33% and 27.91%, respectively. ARM-4 is confirmed to be better than other methods also for 2658 gray scale images. RS-diagram steganalysis conducted complies with DE evaluation results.