Q-adic Transform revisited
| dc.creator | Dumas, Jean-Guillaume | |
| dc.date | 2007-10-02 | |
| dc.date | 2008-06-23 | |
| dc.date.accessioned | 2026-07-07T09:45:45Z | |
| dc.date.available | 2026-07-07T09:45:45Z | |
| dc.description | We present an algorithm to perform a simultaneous modular reduction of several residues. This algorithm is applied fast modular polynomial multiplication. The idea is to convert the $X$-adic representation of modular polynomials, with $X$ an indeterminate, to a $q$-adic representation where $q$ is an integer larger than the field characteristic. With some control on the different involved sizes it is then possible to perform some of the $q$-adic arithmetic directly with machine integers or floating points. Depending also on the number of performed numerical operations one can then convert back to the $q$-adic or $X$-adic representation and eventually mod out high residues. In this note we present a new version of both conversions: more tabulations and a way to reduce the number of divisions involved in the process are presented. The polynomial multiplication is then applied to arithmetic in small finite field extensions. | |
| dc.description | International Symposium on Symbolic and Algebraic Computation 2008, Hagenberg : Autriche (2008) | |
| dc.identifier | https://arxiv.org/abs/0710.0510 | |
| dc.identifier | http://arxiv.org/abs/0710.0510 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/163298 | |
| dc.subject | Symbolic Computation | |
| dc.title | Q-adic Transform revisited | |
| dc.type | text |