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W1984842015 abstract "We present an $r$ -th root extraction algorithm over a finite field $mathbb {F}_q$ . Our algorithm precomputes a primitive $r^s$ -th root of unity $xi$ where $s$ is the largest positive integer satisfying $r^s| q-1$ , and is applicable for the cases when $s$ is small. The proposed algorithm requires one exponentiation for the $r$ -th root computation and is favorably compared to the existing algorithms." @default.
W1984842015 created "2016-06-24" @default.
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W1984842015 date "2016-01-01" @default.
W1984842015 modified "2023-09-24" @default.
W1984842015 title "On <inline-formula><tex-math>$r$</tex-math><alternatives> <inline-graphic xlink:type=simple xlink:href=kwon-ieq1-2417562.gif/></alternatives></inline-formula>-th Root Extraction Algorithm in <inline-formula><tex-math>$mathbb {F}_q$</tex-math><alternatives><inline-graphic xlink:type=simple xlink:href=kwon-ieq2-2417562.gif/> </alternatives></inline-formula> for <inline-formula><tex-math>$qequiv lr^{s}+1;({mathrm mod}; r^{s+1})$</tex-math> <alternatives><inline-graphic xlink:type=…" @default.
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W1984842015 doi "https://doi.org/10.1109/tc.2015.2417562" @default.
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