Arithmetic Operations in the Polynomial Modular Number System
Arithmetic Operations in the Polynomial Modular Number System
Arithmetic Operations in the Polynomial Modular Number System
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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
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