Scaling an RNS number using the core function

We introduce a method for extracting the core of a residue number system (RNS) number within the RNS, this affording a new method for scaling RNS numbers. Suppose an RNS comprises a set of coprime moduli, m_i, with Πm_i=M. We describe a method for approximately scaling such an RNS number by a subset of the moduli, Πm_j=M_J≈√M, with the characteristic that all computations are performed using the original moduli and one other nonmaintained short wordlength modulus.