Geodesic
Analysis of Digital Expansions of Minimal Weight
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12), DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12) (2012).

Voir la notice de l'article provenant de la source Episciences

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. 
@article{DMTCS_2012_special_262_a30,
     author = {Heigl, Florian and Heuberger, Clemens},
     title = {Analysis of {Digital} {Expansions} of {Minimal} {Weight}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12)},
     year = {2012},
     doi = {10.46298/dmtcs.3009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3009/}
}
TY  - JOUR
AU  - Heigl, Florian
AU  - Heuberger, Clemens
TI  - Analysis of Digital Expansions of Minimal Weight
JO  - Discrete mathematics & theoretical computer science
PY  - 2012
VL  - DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12)
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3009/
DO  - 10.46298/dmtcs.3009
LA  - en
ID  - DMTCS_2012_special_262_a30
ER  - 
%0 Journal Article
%A Heigl, Florian
%A Heuberger, Clemens
%T Analysis of Digital Expansions of Minimal Weight
%J Discrete mathematics & theoretical computer science
%D 2012
%V DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12)
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3009/
%R 10.46298/dmtcs.3009
%G en
%F DMTCS_2012_special_262_a30
Heigl, Florian; Heuberger, Clemens. Analysis of Digital Expansions of Minimal Weight. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12), DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12) (2012). doi : 10.46298/dmtcs.3009. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3009/

Cité par Sources :