Stretching definition of pseudo random number generator

Question

I am wondering if someone can say if the following qualifies as a PRNG. Input a random bit seed of length $n$ into the generator, and over $k$ steps the generator uses $k$ publicly known integers to compute the pseudo random bit sequence, outputting a stream of $kn$ pseudo random bits.

I am wondering if the use of the $k$ (predefined) integers in computation still qualifies as a pseudo random number generator; if the integers need not be private, and need not be determined by the user do they count as part of the seed?

Answer 1

The PRNG definition is quite simple. The following two distributions should be indistinguishable

$D_1() : Y \leftarrow \{0,1\}^m$; Return $Y;$

$D_2() : K\leftarrow \{0,1\}^\kappa$; Return $G(K)$;

Here, $G:\{0,1\}^\kappa \rightarrow \{0,1\}^m $is your PRNG function. It is required that the adversary knows everything about G, including the values you refer to. The only thing the adversary does not know is K.

A function is a PRNG if an (polynomial time) adversary who has oracle access to $D_i()$ can not tell if they are interacting with $D_1$ or $D_2$.

So yes, it's OK to have your numbers. They are simply part of the description of the PRNG.