Abstract
Although scalar multiplication is highly fundamental to elliptic curve cryptography (ECC), it is the most time-consuming operation. The performance of such scalar multiplication depends on the performance of its scalar recoding which can be measured in terms of the time and memory consumed, as well as its level of security. This paper focuses on the conversion of binary scalar key representation into {0, 1, 3}-NAF non-adjacent form. Thus, we propose an improved {0, 1, 3}-NAF lookup table and mathematical formula algorithm which improves the performance of {0, 1, 3}-NAF algorithm. This is achieved by reducing the number of rows from 15 rows to 6 rows, and reading two (instead of three) digits to produce one. Furthermore, the improved lookup table reduces the recoding time of the algorithm by over 60% with a significant reduction in memory consumption even with an increase in key size. Specifically, the improved lookup table reduces the memory consumption by as much as 75% for the big key, which shows its higher level of resilience to side channel attacks.
Highlights
Elliptic curves cryptosystem (ECC) was proposed by NealKoblitz and Victor Miller independently in 1985 to design the public-key cryptographic system [1]
ECC is implemented in smart card because of its smaller key size and less computational complexity relative to RSA cryptosystem [2]
Many researchers have tried to improve the performance of the scalar multiplication by representing in other forms with minimal hamming weight [4]
Summary
Koblitz and Victor Miller independently in 1985 to design the public-key cryptographic system [1]. ECC is implemented in smart card because of its smaller key size and less computational complexity relative to RSA cryptosystem [2]. The scalar multiplication involves computing where is an integer and P, Q are points on an elliptic curve It is performed by repeating point addition/subtraction and point doubling operations. Hamming weight of scalar involves the number of the non-zero digits As such, it determines the number of the required point addition/subtraction operation. Many researchers have tried to improve the performance of the scalar multiplication by representing in other forms with minimal hamming weight [4]. It increases the value [6], which implies more time and memory is consumed as it requires more operation during pre-computation.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal of Advanced Computer Science and Applications
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
