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 />
The RED algorithm<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 ke<br />
Algorithm<br />
1 V = U2 ks−1 + L<br />
2 U ← Table(U)<br />
3 R ← U + L<br />
Output<br />
A vector R ≡ V with ‖R‖ ∞ < 2 ks<br />
Jean-Claude Bajard, Laurent Imbert, Thomas Plantard, 28 june 2005 16/18
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