## 3 Proposed Work
### Watermark Embedding and Extraction  
In the proposed scheme, IWT-SVD hybrid transform is applied on the cover image (C) of size \(M\times N\). A binary watermark (W) of size \(P\times Q\) is encrypted and embedded randomly in the low entropy non-overlapping blocks of the cover image to achieve higher imperceptibility, robustness, and security. A block diagram of the proposed watermark embedding is shown in Figure 1. The steps for watermark embedding are provided in Algorithm 1 and explained as follows:  
Watermark Embedding: Firstly, 1-IWT transform is applied on C to obtain LL, LH, HL and HH sub-bands. IWT is applied to achieve higher imperceptibility as well as higher robustness against compression algorithms and filtering. The LL sub-band containsapproximate sub-images, whereas LH, HL and HH sub-bands have fringe information of the image. Therefore, LH and HL sub-bands are selected for watermark embedding. The selected LH and HL sub-bands are divided into \(4\times 4\) blocks, and block-wise entropy is calculated and stored in a vector \(\mathbb{V}\). Image entropy is the randomness measure, and it is used to characterize the texture of the image. The relation used for calculating the image entropy is as follows:  
\[Entropy=-\sum_{i=1}^{256}PB_{i}\,log_{2}\,PB_{i} \tag{1}\]  
where PB is the normalized histogram count of an image. Furthermore, LH and HL sub-bands are decomposed by applying SVD to \(U_{LH}\), \(S_{LH}\), \(V_{LH}\), and \(U_{HL}\), \(S_{HL}\), \(V_{HL}\) sub-matrices, respectively [35]. SVD is applied to achieve robustness against filtering attack, addition of noise, histogram equalization, and geometric attacks. \(S_{LH}\) and \(S_{HL}\) are divided into \(4\times 4\) blocks. Watermark bits are embedded in selected blocks of \(S_{LH}\) and \(S_{HL}\). Block selection is done according to vector \(\mathbb{V}\) i.e., the \(4\times 4\) blocks in \(S_{LH}\) and \(S_{HL}\) having corresponding lower entropy in \(4\times 4\) blocks of LH and HL, respectively, are selected for embedding and called \(B_{LH}\) and \(B_{HL}\). A low entropy block is selected for embedding to ensure higher imperceptibility. Watermark is partitioned into even and odd pixel vectors followed by encryption to obtain encrypted watermark vectors as explained in Section 3.2. Encrypted odd and even watermark pixels are embedded in \(B_{LH}\) and \(B_{HL}\), respectively. Thus, the number of \(B_{LH}\) and \(B_{HL}\) blocks is equal to \(P\times Q/2\). Embedding positions (\(P_{1},P_{2}\)) are determined randomly in the selected low entropy block based on a random sequence generated by a Blum-Blum-Shub (BBS) Pseudo random generator. BBS is deterministic in nature and has a one-way function; hence, it is difficult to break. BBS generates a Pseudo random number series by using initial seed value. For selection of seed value, the following conditions must be satisfied:  
1. Select two prime numbers 'a' and 'b' and both are congruent to a(mod b). 2. Calculate the product of 'a' and 'b', say m. i.e., \(m=a\times b\). 3. Find integer as a co-prime for m, which is taken as the seed value (\(Z_{n}\)). The formula for generating BBS Pseudo random series as shown in Equation (2):  
\[Z_{n}=Z_{n-1}^{2}\,\,mod\,\,m \tag{2}\]  
where \(Z_{n}\) is the \(n\)th term of BBS series and n is any positive integer. \(Z_{1}\) is seed value and \(m=a\times b\). The initial values required for BBS series generation are seed value (s) and m. The generation of BBS Pseudo random series is demonstrated in the following example:  
Example of BBS approach:  
Let us consider that a = 11 and b = 19 are two large prime numbers. \(m=11\times 19=209\).