Efficient Double Bases for Scalar Multiplication
Résumé
In this paper we present efficient algorithms to take advantage of
the double-base number system in the context of elliptic curve
scalar multiplication. We propose a generalized version of Yao's
exponentiation algorithm allowing the use of general double-base
expansions instead of the popular double base chains. We introduce
a class of constrained double base expansions and prove that the
average density of non-zero terms in such expansions is
$O\left(\frac{\log k}{\log \log k}\right)$ for any large integer
$k$. We also propose an efficient algorithm for computing
constrained expansions and finally provide a comprehensive
comparison to double-base chain expansions, including a large
variety of curve shapes and various key sizes.
Mots clés
Equations
Jacobian matrices
Shape
Double-base number system
Yao’s algorithm
point scalar multiplication
elliptic curve scalar multiplication
double-base chain expansions
double bases
constrained expansions
Yao exponentiation algorithm
number theory
general double-base expansions
scalar multiplication
Computational efficiency
Context
Domaines
Cryptographie et sécurité [cs.CR]Origine | Fichiers produits par l'(les) auteur(s) |
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