Computer Science – Symbolic Computation
Scientific paper
2007-10-02
Computer Science
Symbolic Computation
International Symposium on Symbolic and Algebraic Computation 2008, Hagenberg : Autriche (2008)
Scientific paper
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.
No associations
LandOfFree
Q-adic Transform revisited does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Q-adic Transform revisited, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Q-adic Transform revisited will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-7238