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» Algorithms for Exponentiation in Finite Fields
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CORR
2010
Springer
137views Education» more  CORR 2010»
13 years 7 months ago
State Elimination Ordering Strategies: Some Experimental Results
Recently, the problem of obtaining a short regular expression equivalent to a given finite automaton has been intensively investigated. Algorithms for converting finite automata to...
Nelma Moreira, Davide Nabais, Rogério Reis
DAGSTUHL
2006
13 years 9 months ago
Upper and Lower Bounds on Sizes of Finite Bisimulations of Pfaffian Dynamical Systems
In this paper we study a class of dynamical systems defined by Pfaffian maps. It is a sub-class of o-minimal dynamical systems which capture rich continuous dynamics and yet can be...
Margarita V. Korovina, Nicolai Vorobjov
CORR
2008
Springer
125views Education» more  CORR 2008»
13 years 7 months ago
Simultaneous Modular Reduction and Kronecker Substitution for Small Finite Fields
We present algorithms to perform modular polynomial multiplication or modular dot product efficiently in a single machine word. We pack polynomials into integers and perform sever...
Jean-Guillaume Dumas, Laurent Fousse, Bruno Salvy
FOCS
1998
IEEE
13 years 11 months ago
Unsatisfiable Systems of Equations, Over a Finite Field
The properties of any system of k simultaneous equations in n variables over GF(q), are studied, with a particular emphasis on unsatisfiable systems. A general formula for the num...
Alan R. Woods
ASAP
2004
IEEE
141views Hardware» more  ASAP 2004»
13 years 11 months ago
Evaluating Instruction Set Extensions for Fast Arithmetic on Binary Finite Fields
Binary finite fields GF(2n ) are very commonly used in cryptography, particularly in publickey algorithms such as Elliptic Curve Cryptography (ECC). On word-oriented programmable ...
A. Murat Fiskiran, Ruby B. Lee