Arithmetic Operations in the Polynomial Modular Number System
Arithmetic Operations in the Polynomial Modular Number System
Arithmetic Operations in the Polynomial Modular Number System
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
LIRMM<br />
General Coefficient Reduction<br />
<strong>Modular</strong> <strong>Arithmetic</strong><br />
Introduction<br />
New <strong>Number</strong> <strong>System</strong><br />
<strong>Number</strong> system<br />
Adapted <strong>Modular</strong> <strong>Number</strong> <strong>System</strong><br />
Fundamental Theorem<br />
<strong>Arithmetic</strong> on PMNS<br />
<strong>Modular</strong> Multiplication<br />
Coefficient Reduction<br />
The RED Algorithm<br />
Conclusions<br />
Input<br />
A vector V with ‖V ‖ ∞ < 2 t<br />
Algorithm<br />
1 R ← V<br />
2 WHILE t > k s DO<br />
1 R = R2 t−ke + R<br />
2 R ← RED(R)<br />
3 R ← R2 t−ke + R<br />
4 t ← t − (k e − k s)<br />
Output<br />
A vector R ≡ V<br />
With coefficients<br />
‖R‖ ∞ < ρ = 2 ks<br />
Jean-Claude Bajard, Laurent Imbert, Thomas Plantard, 28 june 2005 15/18