Improved Scalar Multiplication Algorithm in Affine Coordinate System using Elliptic Net

Authors

  • Zuren Razali, Norliana Muslim, Saliyah Kahar, Faridah Yunos, Kamsiah Mohamed

DOI:

https://doi.org/10.17762/msea.v71i3.1506

Abstract

Abstract. In elliptic curve encryption, scalar multiplication (SM) is the most expensive and time-consuming operation. The elliptic curve cryptography attracts interest since it offers the same high security with a lower key length, owing to the advancement of modern technologies. Thus, this study designed a new scalar multiplication algorithm using six blocks of the elliptic net in a double and double-add method that cost 12M+6S in each block. This study also proposed a new formula for double block via the elliptic net method that saves four multiplications and four squaring from the prior double step. Experimental results over prime field p were conducted using safe curves namely numsp384t1 and numsp512t1, with equivalence sequences that satisfied gcd(p-1, 3). In the case of the 384-bits, results indicate that the developed scalar multiplication algorithm accelerates the running time by 65.96 % compared to the binary method, 44.81 % compared to the elliptic net without equivalent sequences, 30.28 % compared to the elliptic net with temporary variables, and 19.71 % compared to the seven blocks of the elliptic net with Karatsuba method. In a similar comparison for the 512-bits case, the proposed algorithm attained are 67.23 %, 44.65 %, 30.37 %, and 22.64 % faster, respectively.

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Published

2023-01-09

How to Cite

Zuren Razali, Norliana Muslim, Saliyah Kahar, Faridah Yunos, Kamsiah Mohamed. (2023). Improved Scalar Multiplication Algorithm in Affine Coordinate System using Elliptic Net. Mathematical Statistician and Engineering Applications, 71(3), 1775–1788. https://doi.org/10.17762/msea.v71i3.1506

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Section

Articles