Two Lower Bounds For Shortest Double-Base Number System

Parinya Chalermsook,Hiroshi Imai,Vorapong Suppakitpaisarn

IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES（2015）

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摘要

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 Theta(log n/log log n). Also, we show that the number of terms in the shortest double-base chain is Theta(log n).

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关键词

analysis of algorithms, number representation, elliptic curve cryptography, double-base number system, double-base chain

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