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Modular Arithmetic Using Low Order Redundant Bases
May 1997 (vol. 46 no. 5)
pp. 611-616

AbstractN-digit, radix-α bases are proposed for VLSI implementation of redundant arithmetic, mod m, where

$$\Big\langle {\alpha ^N} \Big\rangle _m=\pm 1, \Big\langle {\alpha ^j} \Big\rangle _m\ne \pm 1,$$

for 0 < j < N and m is prime. These bases simplify arithmetic overflow and are well suited to redundant arithmetic. The representations provide competitive, multiplierless T-point Number Theoretic Transforms, mod m, where T | N or T | 2N.

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Index Terms:
Modular arithmetic, redundant number systems, number theoretic transforms, residue and polynomial number systems.
Citation:
M.g. Parker, M. Benaissa, "Modular Arithmetic Using Low Order Redundant Bases," IEEE Transactions on Computers, vol. 46, no. 5, pp. 611-616, May 1997, doi:10.1109/12.589237
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