Optimal Algorithms for Multiplication in Certain Finite Fields Using Elliptic Curves
From MaRDI portal
Publication:4027853
DOI10.1137/0221071zbMath0778.11075OpenAlexW2117506096MaRDI QIDQ4027853
Publication date: 9 March 1993
Published in: SIAM Journal on Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/0221071
existencebilinear complexityfinite field extensionelliptic curves over finite fieldsChudnovsky algorithmcomplexity of bilinear multiplicationoptimal multiplication algorithm
Analysis of algorithms and problem complexity (68Q25) Number-theoretic algorithms; complexity (11Y16) Elliptic curves (14H52)
Related Items (22)
An improvement of the construction of the D. V. and G. V. Chudnovsky algorithm for multiplication in finite fields ⋮ Optimization of the scalar complexity of Chudnovsky\(^2\) multiplication algorithms in finite fields ⋮ Non-minimum tensor rank Gabidulin codes ⋮ On some bounds for symmetric tensor rank of multiplication in finite fields ⋮ Normal bases from 1-dimensional algebraic groups ⋮ Tower of algebraic function fields with maximal Hasse-Witt invariant and tensor rank of multiplication in any extension of \(\mathbb{F}_2\) and \(\mathbb{F}_3\) ⋮ On the tensor rank of multiplication in any extension of \(\mathbb F_2\) ⋮ The equivariant complexity of multiplication in finite field extensions ⋮ Bilinear complexity of algebras and the Chudnovsky-Chudnovsky interpolation method ⋮ Multiplication algorithm in a finite field and tensor rank of the multiplication. ⋮ On the tensor rank of the multiplication in the finite fields ⋮ Gaps between prime numbers and tensor rank of multiplication in finite fields ⋮ An optimal algorithm for multiplication in \(\mathbb{F}_{256}/\mathbb{F}_ 4\) ⋮ On multiplication in finite fields ⋮ On the bounds of the bilinear complexity of multiplication in some finite fields ⋮ On the construction of elliptic Chudnovsky-type algorithms for multiplication in large extensions of finite fields ⋮ On the bilinear complexity of the multiplication in small finite fields ⋮ Elliptic periods for finite fields ⋮ Curves with many points and multiplication complexity in any extension of \(\mathbb{F}_q\) ⋮ On the tensor rank of multiplication in finite extensions of finite fields and related issues in algebraic geometry ⋮ New uniform and asymptotic upper bounds on the tensor rank of multiplication in extensions of finite fields ⋮ Quasi-optimal algorithms for multiplication in the extensions of \(\mathbb F_{16}\) of degree 13, 14 and 15
This page was built for publication: Optimal Algorithms for Multiplication in Certain Finite Fields Using Elliptic Curves