Incompletely specified numbers in the residue number system-definition and applications

Abstract

Incompletely specified numbers in the residue number system (RNS) are defined in order to make multiplicative inverse computation of a number regardless of its magnitude possible. Incompletely specified RNS is the general RNS model in which completely specified numbers are the special case. Two efficient algorithms for transformation of incompletely to completely specified RNS numbers are shown. Examples of their application in divisibility testing and integer matrix inversion are described.<>