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New Multipliers Modulo 2/sup N/-1
August 1992 (vol. 41 no. 8)
pp. 957-961

Techniques for computing the product of two N-bit integers modulo 2/sup N/-1 from their k-bit byte decompositions are presented. A modulus 2/sup N/-1 is chosen, as multiplication performed in this modulus can be reconstructed from the cyclic convolution between the sequences of the k-bit bytes of the decomposed numbers. It is shown that cyclic convolutions can be computed using only additions and squaring operations but not two-operand multiplications. Since the squaring operation is a one-operand operation, significant savings in ROM bits can be obtained if look-up tables are used.

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Index Terms:
multipliers; modulo 2/sup N/-1; multiplication; cyclic convolution; additions; squaring; ROM bits; look-up tables; digital arithmetic; multiplying circuits.
A. Skavantzos, P.B. Rao, "New Multipliers Modulo 2/sup N/-1," IEEE Transactions on Computers, vol. 41, no. 8, pp. 957-961, Aug. 1992, doi:10.1109/12.156538
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