On r -th Root Extraction Algorithm in Fq for q≡lrs+1(modrs+1) with 0<l<r and Small s.

We present an r<alternatives> <inline-graphic xlink:type="simple" xlink:href="kwon-ieq6-2417562.gif"/></alternatives>-th root extraction algorithm over a finite field \mathbb {F}_q<alternatives> <inline-graphic xlink:type="simple" xlink:href="kwon-ieq7-2417562.gif"/></alternatives>. Our algorithm precomputes a primitive r^s$<alternatives><inline-graphic xlink:type="simple" xlink:href="kwon-ieq8-2417562.gif"/> </alternatives>-th root of unity $\xi$<alternatives> <inline-graphic xlink:type="simple" xlink:href="kwon-ieq9-2417562.gif"/></alternatives> where $s$<alternatives><inline-graphic xlink:type="simple" xlink:href="kwon-ieq10-2417562.gif"/></alternatives> is the largest positive integer satisfying $r^s| q-1$<alternatives> <inline-graphic xlink:type="simple" xlink:href="kwon-ieq11-2417562.gif"/></alternatives>, and is applicable for the cases when $s$<alternatives><inline-graphic xlink:type="simple" xlink:href="kwon-ieq12-2417562.gif"/> </alternatives> is small. The proposed algorithm requires one exponentiation for the $r$<alternatives><inline-graphic xlink:type="simple" xlink:href="kwon-ieq13-2417562.gif"/></alternatives> -th root computation and is favorably compared to the existing algorithms. [ABSTRACT FROM AUTHOR]