Analysis of Digital Expansions of Minimal Weight
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2012-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/3009/pdf |
| _version_ | 1797270345556688896 |
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| author | Florian Heigl Clemens Heuberger |
| author_facet | Florian Heigl Clemens Heuberger |
| author_sort | Florian Heigl |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-25T02:02:48Z |
| format | Article |
| id | doaj.art-4d9d0d4630fb4681b575dd143600ade7 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:02:48Z |
| publishDate | 2012-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-4d9d0d4630fb4681b575dd143600ade72024-03-07T14:50:50ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502012-01-01DMTCS Proceedings vol. AQ,...Proceedings10.46298/dmtcs.30093009Analysis of Digital Expansions of Minimal WeightFlorian Heigl0Clemens Heuberger1Graz University of Technology [Graz]Alpen-Adria-Universität Klagenfurt [Klagenfurt, Austria]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.https://dmtcs.episciences.org/3009/pdfdynamic programminglimit distributiondigital expansionshamming weightelliptic curve cryptographyfrobenius endomorphismminimal expansions[info.info-ds] computer science [cs]/data structures and algorithms [cs.ds][info.info-dm] computer science [cs]/discrete mathematics [cs.dm][math.math-co] mathematics [math]/combinatorics [math.co][info.info-cg] computer science [cs]/computational geometry [cs.cg] |
| spellingShingle | Florian Heigl Clemens Heuberger Analysis of Digital Expansions of Minimal Weight Discrete Mathematics & Theoretical Computer Science dynamic programming limit distribution digital expansions hamming weight elliptic curve cryptography frobenius endomorphism minimal expansions [info.info-ds] computer science [cs]/data structures and algorithms [cs.ds] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-cg] computer science [cs]/computational geometry [cs.cg] |
| title | Analysis of Digital Expansions of Minimal Weight |
| title_full | Analysis of Digital Expansions of Minimal Weight |
| title_fullStr | Analysis of Digital Expansions of Minimal Weight |
| title_full_unstemmed | Analysis of Digital Expansions of Minimal Weight |
| title_short | Analysis of Digital Expansions of Minimal Weight |
| title_sort | analysis of digital expansions of minimal weight |
| topic | dynamic programming limit distribution digital expansions hamming weight elliptic curve cryptography frobenius endomorphism minimal expansions [info.info-ds] computer science [cs]/data structures and algorithms [cs.ds] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-cg] computer science [cs]/computational geometry [cs.cg] |
| url | https://dmtcs.episciences.org/3009/pdf |
| work_keys_str_mv | AT florianheigl analysisofdigitalexpansionsofminimalweight AT clemensheuberger analysisofdigitalexpansionsofminimalweight |