Cryptology ePrint Archive: Report 2013/209

New modular multiplication and division algorithms based on continued fraction expansion

Mourad Gouicem

Abstract: In this paper, we apply results on number systems based on continued fraction expansions to modular arithmetic. We provide two new algorithms in order to compute modular multiplication and modular division. The presented algorithms are based on the Euclidean algorithm and are of quadratic complexity.

Category / Keywords: foundations / Modular arithmetic – Continued fraction – Euclidean algorithm – Ostrowski number system

Date: received 11 Apr 2013, last revised 11 Apr 2013

Contact author: mourad gouicem at lip6 fr

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Version: 20130414:153345 (All versions of this report)

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