A hybrid addition chain method for faster scalar multiplication

Mohamad Afendee, Mohamed and Mohamad Rushdan, Md Said (2015) A hybrid addition chain method for faster scalar multiplication. WSEAS Transactions on Communications, 14 (19). pp. 144-152. ISSN 1109-2742

[img] Text
Restricted to Registered users only

Download (278kB)


Solutions to addition chain problem can be applied to operations involving huge number such as scalar multiplication in elliptic curve cryptography. Recently, a decomposition method was introduced, with an intention to generate addition chain with minimal possible terms. Totally different from others, this new method uses rule representation for prime factors of n, and a new algorithm to generate a complete chain for n. Although the chain is not always optimal, the method is shown to outclass other existing methods for certain cases of n. The method is based on prime power decomposition and it can be seen as a two-layered approach, prime layer and prime power layer. In this paper, we adapt an idea of non-adjacent form into decomposition method at prime layer. This new hybrid method is called signed decomposition method. Our objective is to reduce the number of addition operations for each p by transforming an original unsigned rule into a signed rule. The study shows that the length of this new chain is confined to the same boundary as that of an optimal chain. A series of tests shows that our method outperforms decomposition method as well as earlier methods significantly. Moreover, possible saving of terms can be made more noticeable as we increase the prime factor.

Item Type: Article
Uncontrolled Keywords: decomposition method, elliptic curve cryptography, non-adjacent form, binary method, NP-hard
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisions: Faculty of Informatics & Computing
Depositing User: Fatin Safura
Date Deposited: 03 Feb 2022 04:27
Last Modified: 03 Feb 2022 04:27
URI: http://eprints.unisza.edu.my/id/eprint/5033

Actions (login required)

View Item View Item