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» Algorithms for Exponentiation in Finite Fields
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111
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CORR
2010
Springer
137views Education» more  CORR 2010»
15 years 2 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
112
Voted
DAGSTUHL
2006
15 years 3 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
117
Voted
CORR
2008
Springer
125views Education» more  CORR 2008»
15 years 1 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
15 years 6 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»
15 years 5 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