[Resource Topic] 2004/353: Direct Division in Factor Rings

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Direct Division in Factor Rings

Authors: Patrick Fitzpatrick, Christopher Wolf


Conventional techniques for division in the polynomial factor ring
\Ftm or the integer ring \Zzs use a combination of inversion
and multiplication. We present a new algorithm that computes the
division directly and therefore eliminates the multiplication
step. The algorithm requires 2\,{\rm degree\/}{(m)} (resp. 2 \log_2 n) steps, each of which uses only shift and
multiply-subtract operations.

ePrint: https://eprint.iacr.org/2004/353

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