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Analysis on Yu et al.'s dynamic algorithm for canonic DBC
- Title
- Analysis on Yu et al.'s dynamic algorithm for canonic DBC
- Authors
- Eom, Sookyung; Lee, Hyang-Sook; Lim, Seongan; Song, Kyunghwan
- Ewha Authors
- 이향숙; 임선간; 엄수경
- SCOPUS Author ID
- 이향숙; 임선간; 엄수경
- Issue Date
- 2021
- Journal Title
- DISCRETE APPLIED MATHEMATICS
- ISSN
- 0166-218X
1872-6771
- Citation
- DISCRETE APPLIED MATHEMATICS vol. 294, pp. 31 - 40
- Keywords
- Double-base chain; Scalar multiplication; Hamming weight
- Publisher
- ELSEVIER
- Indexed
- SCIE; SCOPUS
- Document Type
- Article
- Abstract
- Recently, Yu et al. presented an algorithm for a canonic DBC of a positive integer n by solving certain subproblems recursively and it requires O((log n)(2)log log n) bit operations and O((log n)(2)) bits of memory. This is currently the most efficient recoding type algorithm for canonic DBCs when balanced computing power and memory are available. In this paper, we present a memory efficient algorithm to compute a nearly DBC from the idea of Yu et al. We present a simple overview of Yu et al.'s algorithm focusing on canonic DBC and refine Yu et al.'s proof for range of the leading term of canonic DBCs. By using the refined range, we suggest how to improve the efficiency of Yu et al.'s algorithm computationally and present an algorithm for nearly canonic DBC with memory requirement O(log n). We also present experimental comparison on the Hamming weights of Yu et al.'s algorithm, tree based algorithm, the classic greedy DBC algorithm, and our memory efficient algorithm. (C) 2021 Elsevier B.V. All rights reserved.
- DOI
- 10.1016/j.dam.2021.01.023
- Appears in Collections:
- 자연과학대학 > 수학전공 > Journal papers
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