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» Algorithms for Exponentiation in Finite Fields
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ISSAC
2004
Springer
102views Mathematics» more  ISSAC 2004»
14 years 27 days ago
FFPACK: finite field linear algebra package
The FFLAS project has established that exact matrix multiplication over finite fields can be performed at the speed of the highly optimized numerical BLAS routines. Since many a...
Jean-Guillaume Dumas, Pascal Giorgi, Clémen...
TEC
2008
93views more  TEC 2008»
13 years 7 months ago
An Artificial Immune System Heuristic for Generating Short Addition Chains
This paper deals with the optimal computation of finite field exponentiation, which is a well-studied problem with many important applications in the areas of error-correcting code...
Nareli Cruz Cortés, Francisco Rodríg...
SODA
2004
ACM
88views Algorithms» more  SODA 2004»
13 years 9 months ago
Constructing finite field extensions with large order elements
In this paper, we present an algorithm that given a fixed prime power q and a positive integer N, finds an integer n [N, 2qN] and an element Fqn of order greater than 5.8n/ log...
Qi Cheng
ISSAC
1997
Springer
138views Mathematics» more  ISSAC 1997»
13 years 11 months ago
Fast Polynomial Factorization Over High Algebraic Extensions of Finite Fields
New algorithms are presented for factoring polynomials of degree n over the finite field of q elements, where q is a power of a fixed prime number. When log q = n1+a , where a ...
Erich Kaltofen, Victor Shoup
MOC
2000
111views more  MOC 2000»
13 years 7 months ago
Voronoi's algorithm in purely cubic congruence function fields of unit rank 1
The first part of this paper classifies all purely cubic function fields over a finite field of characteristic not equal to 3. In the remainder, we describe a method for computing ...
Renate Scheidler, Andreas Stein