Issue No. 08 - August (1992 vol. 41)

ISSN: 0018-9340

pp: 957-961

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/12.156538

ABSTRACT

<p>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.</p>

INDEX TERMS

multipliers; modulo 2/sup N/-1; multiplication; cyclic convolution; additions; squaring; ROM bits; look-up tables; digital arithmetic; multiplying circuits.

CITATION

P.B. Rao, A. Skavantzos, "New Multipliers Modulo 2/sup N/-1",

*IEEE Transactions on Computers*, vol. 41, no. , pp. 957-961, August 1992, doi:10.1109/12.156538