## Cryptology ePrint Archive: Report 2020/1041

Abraham Westerbaan and Bas Westerbaan

Abstract: Often in cryptography one needs to make a consistent choice of square root in a finite field. We show that such a choice is equivalent to providing a reasonable sign function. Then we show that for $\mathbb{F}_{p^k}$ (with odd prime $p \neq 1$ and $k\neq 0$) such a sign function exists if and only if $k$ is odd.

Category / Keywords: foundations / finite fields, square root, sign function