New modulo decomposed residue-to-binary algorithm for general moduli sets

We propose a new modulo arithmetic theorem to decompose the base of modulo operations. This new theorem has been used to reduce further the modulo size of the modified CRT (Chinese remainder theorem) for general moduli sets. Furthermore, we have applied the modulo decomposition technique and the modulo improved CRT to derive a R/B (residue-to-binary) converter algorithm for a newly found three-moduli set, M={2ⁿ-1,2ⁿ, 2^n-1-1}. In comparison to the modified CRT, the improved CRT can cut the modulo size by half and reduce the length of the modulo operator in terms of 36%.