Algorithm 4 Pseudo random key generation from Random key.

Require:  Random key (128 bits) Ensure:  Pseudo Random key ($(P\times Q$)/2 ) 1: Initial conditions $a_0$, $b_0$, $S_1$ and $S_2$ are generated as follows: $$a_0=\sum _{K=1}^{20}\frac{Randomkey(K)}{2^K}$$ $$b_0=(\sum _{K=21}^{50}\frac{Randomkey(K)}{2^{K-52}})mod1$$ $$\begin{array}{cc}\hfill S_1=& (\sum _{K=1}^{8}Randomkey(K)\times 2^K\hfill \\ & +\sum _{K=25}^{76}\frac{Randomkey(K)}{2^{K-24}}+b_0)mod10+10\hfill \end{array}$$ $$\begin{array}{cc}\hfill S_2=& (\sum _{K=121}^{128}Randomkey(129-K)\times 2^K\hfill \\ & +\sum _{K=77}^{128}\frac{Randomkey(K)}{2^{K-76}}\times S_1)mod10+10\hfill \end{array}$$ $$a_0=(a_0+S_2)mod1$$ 2: The initial values $a_0,S_{1}and{b}_0,S_2$ are used for the logistic and sine map, respectively. The maps are iterated $P\times Q$ times, whereby the random sequences are stored as matrices LF and SF of size $P\times Q$ as $$\begin{array}{cc}\hfill LF=& mod((power(S_1,2)\times a_0\hfill \\ & \times (1-S_1\ast a_0)+\frac{S_1}{a_0}),1)\hfill \end{array}$$ $$\begin{array}{cc}\hfill SF=& mod((S_2\ast sin(180\ast S_2\ast b_0)\hfill \\ & +\frac{S_2}{b_0},1)\hfill \end{array}$$ 3: Based on these intermediary matrices, a final Pseudo random key $P{R}_{Key}$ is then calculated as $$\begin{array}{c}\hfill P{R}_{key}=\sum _{k=1}^P\sum _{l=1}^Q(((LF(k,l)+SF(k,l)))mod10)\end{array}$$ where LF(k, l) and SF(k, l) are the elements of the LF and SF matrices, respectively, while k and l denote the row and column of LF. The resulting matrix $P{R}_{key}$ is Pseudo random key in the range of $[1,\frac{(P\times Q)}{2}]$, where $P\times Q$ is the size of the watermark image.