episciences.org_3009_20230328192221617
20230328192221617
episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
Discrete Mathematics & Theoretical Computer Science
13658050
01
01
2012
DMTCS Proceedings vol. AQ,...
Proceedings
Analysis of Digital Expansions of Minimal Weight
Florian
Heigl
Clemens
Heuberger
Extending an idea of Suppakitpaisarn, Edahiro and Imai, a dynamic programming approach for computing digital expansions of minimal weight is transformed into an asymptotic analysis of minimal weight expansions. The minimal weight of an optimal expansion of a random input of length $\ell$ is shown to be asymptotically normally distributed under suitable conditions. After discussing the general framework, we focus on expansions to the base of $\tau$, where $\tau$ is a root of the polynomial $X^2 \mu X + 2$ for $\mu \in \{ \pm 1\}$. As the Frobenius endomorphism on a binary Koblitz curve fulfils the same equation, digit expansions to the base of this $\tau$ can be used for scalar multiplication and linear combination in elliptic curve cryptosystems over these curves.
01
01
2012
3009
https://hal.science/hal01197230v1
10.46298/dmtcs.3009
https://dmtcs.episciences.org/3009

https://dmtcs.episciences.org/3009/pdf

https://dmtcs.episciences.org/3009/pdf