computational complexity

, Volume 22, Issue 3, pp 463–516 | Cite as

Modular Composition Modulo Triangular Sets and Applications

Article

Abstract

We generalize Kedlaya and Umans’ modular composition algorithm to the multivariate case. As a main application, we give fast algorithms for many operations involving triangular sets (over a finite field), such as modular multiplication, inversion, or change of order. For the first time, we are able to exhibit running times for these operations that are almost linear, without any overhead exponential in the number of variables. As a further application, we show that, from the complexity viewpoint, Charlap, Coley, and Robbins’ approach to elliptic curve point counting can be competitive with the better known approach due to Elkies.

Keywords

Triangular set modular composition power projection finite fields complexity 

Subject classification

68W30 

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© Springer Basel 2013

Authors and Affiliations

  1. 1.LIFL, UMR-CNRS 8022LilleFrance
  2. 2.Computer Science DepartmentThe University of Western, OntarioLondonCanada

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