Shorter addition-subtraction chain with signed composition method
Addition chain is considered as the solution to large number operation of scalar multiplication in elliptic curve cryptosystem. Recently, a decomposition method was introduced as a new technique to generate addition chain with minimal possible terms. The method which is based on prime power input...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
2017
|
| Subjects: | |
| Online Access: | http://eprints.unisza.edu.my/5305/1/FH02-FIK-17-09803.pdf http://eprints.unisza.edu.my/5305/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | Addition chain is considered as the solution to large number operation of scalar
multiplication in elliptic curve cryptosystem. Recently, a decomposition method was introduced as a new
technique to generate addition chain with minimal possible terms. The method which is based on prime
power input form was shown to outclass previous methods under certain condition. An earlier study
shows that this method can also be used with non-prime integer such that found in composition method.
As a result of no extra cost for point negation on elliptic curve, subtraction operation can be included
during the generation of the chain as we found in signed decomposition method. As an alternative, in this
paper, we proposed a signed composition method. Using this method, we study the properties of the chain
against those generated by prime power equivalent. The comparative result between signed composition
method against signed decomposition method shows that by allowing a subtraction information into the
chain, the resulting chains are nearly of equal length which is very different from the unsigned case,
where original decomposition method is by far has outperformed the composition method. |
|---|