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A method for generating a design of a multiplier is disclosed. The method generally includes steps (A) to (C). Step (A) may generate a first circuit comprising a plurality of polynomial results of a particular multiplier scheme based on a plurality of parameters of the multiplier. The first circuit is generally configured to multiply a plurality of polynomials. Step (B) may generate a second circuit comprising a plurality of polynomial evaluators based on the parameters. The second circuit may be (i) connected to the first circuit and (ii) configured to evaluate a polynomial modulo operation. Step (C) may generate the design of the multiplier in combinational logic by optimizing a depth of a plurality of logic gates through the first circuit and the second circuit. A product of the polynomials generally resides in a finite field.