Algebraic complexities and algebraic curves over finite fields
Journal of Complexity
Optimal algorithms for multiplication in certain finite fields using elliptic curves
SIAM Journal on Computing
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
On the Bounds of the Bilinear Complexity of Multiplication in Some Finite Fields
Applicable Algebra in Engineering, Communication and Computing
On multiplication in finite fields
Journal of Complexity
Algebraic Geometry in Coding Theory and Cryptography
Algebraic Geometry in Coding Theory and Cryptography
Curves with Many Points and Multiplication Complexity in Any Extension of Fq
Finite Fields and Their Applications
Finite Fields and Their Applications
Bilinear complexity of algebras and the Chudnovsky-Chudnovsky interpolation method
Journal of Complexity
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In this paper, we obtain new bounds for the tensor rank of multiplication in any extension of F"2. In particular, it also enables us to obtain the best known asymptotic bound. To this aim, we use the generalized algorithm of type Chudnovsky with derivative evaluations on places of degree one, two and four applied on the descent over F"2 of a Garcia-Stichtenoth tower of algebraic function fields defined over F"2"^"4.