My question is related to this question on Cryptography SE.

In the following, all the operations and polynomials are defined over a finite field of prime order, $\mathbb{F}_p$, where $p$ is a sufficiently large prime number. All values and polynomials are non-zero.

Let the degree of each of polynomials $R(x)$, $Z(x)$ and $P(x)$ be $d>1$. Also, let $Z$ and $R$ be two polynomials picked uniformly at random from $\mathbb{F}_p[x]$. Note that $P(x)$ is a fixed polynomial. We set $F(x)=R\cdot P+Z$.

Let's assume we arbitrary change $F(x)$ to $F'(x)$.

Question : Is polynomial $$p'(x)=\frac{F'(x)-Z(x)}{R(x)}$$ a random polynomial uniformly distributed over the polynomial of degree d in $\mathbb{F}_p[x]$?

  • $\begingroup$ @EthanBolker can you please explain in more details? $\endgroup$ – Ay. Oct 17 at 16:26

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