In the paper An Improved Monte Carlo Factorization Algorithm an algorithm is given for factoring numbers. Some values that are used are random. I'm wondering how such values should be chosen? Is truly uniform random the best or are some values better than others?
To my understanding $x_o$ and $m$ can be assigned the initial value randomly from the range $[1, N-1]$ where $N$ is the input number. Also the function $f(x)=x^2+1$ is usually chosen but +1 can be random too. Is there any range?
Is there any other considerations? For example if the algorithm fails on $x_o=m=1$ would it be better to change one at a time or all of them?
Also does anyone have insight on what the variable $m$ actually represents?