Direct Division in Factor Rings

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Paper 2004/353

Direct Division in Factor Rings

Patrick Fitzpatrick and Christopher Wolf

Abstract

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.

Metadata

Available format(s): PDF PS
Category: Implementation
Publication info: Published elsewhere. Electronic Letters 38 No. 21 (2002), pp 1253-1254
Keywords: Division Extended Euclid Elliptic Curves Multivariate Quadratic Public Key
Contact author(s): Christopher Wolf @ esat kuleuven ac be
History: 2004-12-18: revised; 2004-12-13: received; See all versions
Short URL: https://ia.cr/2004/353
License: CC BY