Two Lower Bounds for Shortest Double-Base Number System

Parinya CHALERMSOOK  Hiroshi IMAI  Vorapong SUPPAKITPAISARN  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E98-A   No.6   pp.1310-1312
Publication Date: 2015/06/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E98.A.1310
Type of Manuscript: LETTER
Category: Algorithms and Data Structures
Keyword: 
analysis of algorithms,  number representation,  elliptic curve cryptography,  double-base number system,  double-base chain,  

Full Text: PDF>>
Buy this Article




Summary: 
In this letter, we derive two lower bounds for the number of terms in a double-base number system (DBNS), when the digit set is {1}. For a positive integer n, we show that the number of terms obtained from the greedy algorithm proposed by Dimitrov, Imbert, and Mishra [1] is $Thetaleft( rac{log n}{log log n} ight)$. Also, we show that the number of terms in the shortest double-base chain is Θ(log n).