Modular reduction by multi-level table lookup

Common designs for reducing the lookup table size in modular reduction (computing of residues) all require peripheral logic in the form of multiplexers and/or (multi-operand) adders. We derive optimal two-level modular reduction circuits that are synthesized from lookup tables and pipeline latches only. We compare three such purely tabular realizations in terms of total table size. Extensions to more than two lookup levels, for gaining higher throughput, are also briefly discussed.