A new algorithm for computing triple-base number system

Abstract

We introduce here a generalized method a new Algorithm to find Triple-Base number system and Triple-Base chain and hence in turn Single Digit Triple-Base number system(SDTBNS). The proposed method is not only simpler and faster than the Algorithms to find Double-Base number system or Double-Base chain, experimentally it also returns a shorter length of Triple-Base chain which in turn reduces the size of the look-up-table to find out SDTBNS. The complexity analysis and experimental results shows the novelty of the proposed Algorithm. Moreover when the proposed method is applied to find scalar multiplication in case of Elliptic Curve Cryptography and coefficient multiplication in case of designing digital filter, its efficiency also proves its novelty. Here we have used third base as 5 because when it is multiplied by 2 gives 10 which can be efficiently used for decimal shifting, i.e. if an integer 'n' can be represented in SDTBNS form, then n/10 x or nx10 x can also represented in SDTBNS only by diving or multiplying 'n' by 10.