In $\mathbb{Q}$, $\mathbb{R}$ and $\mathbb{C}$ there are obvious ways to calculate the square root of a quadratic residue. For finite fields of order $p$ we can use the Tonelli–Shanks algorithm. How about for a finite field $\mathbb{F}_{p^q}$ of order $p^q$? Or more general, for a back-box field?
2026-04-08 14:06:43.1775657203
Square root in a general field
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