In Groth-Sahai NIZK proof system, they have defined something called Quadratic Equation in $\mathbb{Z}_n$ as shown below. But, my idea of quadratic equation was a second order polynomial equation in a single variable, something of the form $ax^2 + bx + c = 0$. Then how is the below equation a quadratic one?

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  • $\begingroup$ Of course! It's a quadratric equation in $\mathbb{Z}_n$ but in matrix form. $\endgroup$ – Robert NACIRI Feb 1 '15 at 10:18

$ax^2+bx+c=0$ is the general expression of a quadratic equation in one variable. Here, there are more than one. You may want to look into how the degree of a multivariate polynomial is defined.

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