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Let $R:\mathbb{F}^n \rightarrow \mathbb{F}^m$ be a multivariate quadratic map. Here $\mathbb{F}$ denotes the finite field of order $q$.

I am curious to know whether the distribution of $R(x)$ for uniform $x\in \mathbb{F}^n$ is computationally indistinguishable from uniform.

I was reading a paper and authors assumed this fact. I am attaching the screenshot for your kind reference. Refer to Theorem 2.

Link to the paper https://eprint.iacr.org/2017/131.pdf

enter image description here

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    $\begingroup$ Certainly it is not true for all quadratic maps (consider $\mathbb{F}$ with 3 elements, $n=m=1$ and $R: x \mapsto x^2$), so I guess the question is when you can assume it to be computationally indistinguishable. This Crypto SE question might help: crypto.stackexchange.com/questions/53382/… $\endgroup$
    – Jukka Kohonen
    Feb 4, 2022 at 7:04

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