Algorithm 1 Random-Permutation algorithm

Input: Size of random numbers, n, the polynomial $p\left(x\right)$, $\alpha$, and $\beta$.  Output: S, the random permutation of the integers $\{1,2,\dots ,n\}$.  Step 1: Set $S=1$, $x_0=(\alpha +\beta )/2$, $x=p\left(x_0\right)-fix\left(p\left(x_0\right)\right)$  Step 2: For $i=2$ to n, compute               $S=\left[Si\right]$               $k=ceil(i\ast x)$               $S\left(\right[ki\left]\right)=S\left(\right[ik\left]\right)$               $x_1=x_0-p\left(x_0\right)/p^{\prime }\left(x_0\right)$               $x=p\left(x_1\right)-fix\left(p\left(x_1\right)\right)$               $x_0=x_1$             End For  Step 3: S