Abstract
The most expensive and time-consuming operation in Elliptic curve cryptosystem is scalar multiplication operation. Optimization of scalar multiplication will substantially enhance the ECC performance. Scalar multiplication can be improved by using an enhanced scalar recoding algorithm that can decrease the number of operations in the scalar representation process. The objective of this research is to introduce an efficient design and implementation of {0,1,3}-NAF scalar recoding algorithm by applying block method technique. The base algorithm has a complex look up table. With block method application on base algorithm, a complex look up table is undesired. Instead a fix look up table is introduced with less computation required for recoding. The Big-O notation is used to measure the complexity and (µs) used to evaluate the running time of base and proposed algorithm.
Highlights
The efficiency of scalar multiplication operation has direct effects on the performance of ECC (Kodali et al., 2013)
This computational level involves with scalar representation and scalar recoding technique
In order to recode the scalar into selected number representation the scalar recoding technique is required
Summary
The efficiency of scalar multiplication operation has direct effects on the performance of ECC (Kodali et al., 2013). In order to recode the scalar into selected number representation the scalar recoding technique is required. This technique should reduce the hamming weight of scalar k. Joye and Yen (2002) used different base to represent scalar k. Reducing the Hamming weight will enhance the scalar multiplication performance, since less addition and doubling is required (Shah et al, 2010). Scalar recoding technique is used to recode a scalar k into different representation with less Hamming weight (Yasin et al, 2014). The result of this recoding can have the same magnitude to the scalar or lesser
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