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» FFPACK: finite field linear algebra package
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CORR
2004
Springer
117views Education» more  CORR 2004»
14 years 10 months ago
Efficient dot product over word-size finite fields
We want to achieve efficiency for the exact computation of the dot product of two vectors over word size finite fields. We therefore compare the practical behaviors of a wide range...
Jean-Guillaume Dumas
101
Voted
COCO
2008
Springer
100views Algorithms» more  COCO 2008»
15 years 12 hour ago
Detecting Rational Points on Hypersurfaces over Finite Fields
We study the complexity of deciding whether a given homogeneous multivariate polynomial has a nontrivial root over a finite field. Given a homogeneous algebraic circuit C that com...
Swastik Kopparty, Sergey Yekhanin
76
Voted
TIT
2011
169views more  TIT 2011»
14 years 5 months ago
Network Coding Theory Via Commutative Algebra
—The fundamental result of linear network coding asserts the existence of optimal codes over acyclic networks when the symbol field is sufficiently large. The restriction to just...
Shuo-Yen Robert Li, Qifu Tyler Sun
CORR
2008
Springer
125views Education» more  CORR 2008»
14 years 10 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
122
Voted
CSR
2008
Springer
15 years 7 hour ago
Cryptanalysis of Stickel's Key Exchange Scheme
We offer cryptanalysis of a key exchange scheme due to Stickel [11], which was inspired by the well-known Diffie-Hellman protocol. We show that Stickel's choice of platform (t...
Vladimir Shpilrain