Scaling and reduction in the residue number system with pairs of conjugate moduli

The residue number system (RNS) with pairs of conjugate moduli uses a modulus set containing pairs of moduli of the form {2^k-1, 2^k+1}. This RNS provides a good trade-off between large dynamic range and channel width. It also supports efficient channel-width multiplication and addition as well as efficient conversions between weighted and RNS representations. This paper presents algorithms for exact scaling and Montgomery reduction in the RNS with pairs of conjugate moduli. The ability to perform these operations on very large integers suggest this RNS is suitable for the implementation of public key cryptosystems.