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Design of multi-residue generators using shared logic

The generation of the remainder of the integer division by one or more moduli is essential in various applications involving residue number system (RNS), arithmetic error control coding, and cryptography. In this paper, we consider the possibility of designing multi-residue generators capable of sharing hardware which, unlike previous designs, are not limited to the pairs of conjugate moduli 2a − 1 and 2a−1 + 1only. We show that logic circuitry can be shared by residue generators modulo any moduli whose period or half-period parameters have common divisors and are at least three times larger than the number of inputs of the generators. For some subsets of moduli, over 40% hardware reduction is observed.