Given 2 successive numbers produced by the LCG (Linear Congruential Generator) $x_{n+1} = (a \cdot x_n + c) \bmod m.$, how can I determine the parameters of this LCG? Assuming that $m$ is given.
Given that there are several candidate LCGs, how is possible to find all the possible parameters?
I don't think you can do it with just two. If you know the modulus and have 3 successive values then you can subtract the two equations
$$ x_2 \equiv x_1 * a + c \pmod{m} \\ x_3 \equiv x_2 * a + c \pmod{m} $$
which gives $$ (x_2 - x_3) \equiv (x_1 - x_2)*a \pmod{m} \\ \Rightarrow (x_2 - x_3) * (x_1 - x_2)^{-1} \equiv a \pmod{m} $$
then to get $c$ you can just solve $$ x_2 \equiv x_1 * a + c \pmod{m} \\ \Rightarrow x_2 - x_1*a \equiv c \pmod{m} $$
