By Topic  Improving Euclidean division and modular reduction for
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Bajard, J. ; Univ. Montpellier II, France ; Imbert, L. ;
Plantard, T.  Modular arithmetic is becoming an area of major
importance for many modern applications; RNS is widely used in
digital signal processing, and most public-key cryptographic
algorithms require very fast modular multiplication, and
exponentiation. When such an arithmetic is required, specific
values such as Fermat or Mersenne numbers are often chosen since
they allow for very efficient implementations. However, there
are cases where only very few of those numbers are available. We
present an algorithm for the Euclidean division with remainder
and we give the classes of divisors for which our algorithm is
particularly efficient compared