New modular multiplication and division algorithms based on continued fraction expansion

Mourad Gouicem (1)

1 PEQUAN - Performance et Qualité des Algorithmes Numériques

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.

Mots clés: Modular arithmetic; Continued fraction; Euclidean algorithm; Ostrowski number system

Domaines: Arithmétique des ordinateurs

Mourad Gouicem. New modular multiplication and division algorithms based on continued fraction expansion. 2013. ⟨hal-00800497⟩