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A novel hardware algorithm, a VLSI architecture, and an optimization methodology for residue multipliers are introduced in this paper. The proposed design approach identifies certain properties of the bit products that participate in the residue product computation and subsequently exploits them to reduce the complexity of the implementation. A set of introduced theorems is used to identify the particular properties. The introduced theorems are of significant practical importance because they allow the definition of a graph-based design methodology. In addition, a bit-product weight encoding scheme is investigated in a systematic way, and exploited in order to minimize the number of bit products processed in the proposed multiplier. Performance data reveal that the introduced architecture achieves area × time complexity reduction of up to 55%, when compared to the most efficient previously reported design.