Data Hiding Using Flexible Multi-bit MER

Multi-bit minimum error replacement (MER) is a method that can embed multi-bit logo/secret data into k least-significant bits (LSBs) of cover data only introduces minimum embedding error (MEE). However, k-LSBs MER suffers from weak robustness. Moreover, it is unfortunate because no literature discusses the formulations and the properties of multi-bit MEE up to this day. Therefore, this work proposes a novel new multi-bit MERs with flexible bit location (multi-bit MER_FBL) to overcome the problem of robustness. This work also illustrates the formulations and properties of MEEs in the multi-bit MER_FBL. The MEE can be easily and determinedly evaluated using the proposed formulations and properties. The proposed multi-bit MER_FBL embeds and hides multi-bit (k-bit, k≥1) logo/secret data into any adjoining (starting with the i^th location) k-bit b_ib_i-1⋯b_i-k+1 of cover data only introduces MEE in the range 0 of ±(2^k-1)2^i-k; moreover, its flexible bit location enhances the embedded robustness as robustness increases as the order (location) of embedding bits increases. As the proposed multi-bit MER_FBL can embed multi-bit logo/secret data into any adjoining bits of cover data and has MEE and high robustness, this method was applied for the steganographic and watermarking applications and achieves good embedding quality.