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All Journal International Journal of Advances in Applied Sciences
Abdul Kadir, Mohd Fadzil
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Earth & Planetary Sciences Environmental Science Materials Science & Nanotechnology Mathematics Physics

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Addition chain heuristics in application to elliptic curve cryptosystems Mohamed, Mohamad Afendee; Shawai, Yahaya Garba; Derahman, Mohd Noor; Mamat, Abd Rasid; Mohd Satar, Siti Dhalila; Amri Abidin, Ahmad Faisal; Abdul Kadir, Mohd Fadzil
International Journal of Advances in Applied Sciences Vol 13, No 3: September 2024
Publisher : Institute of Advanced Engineering and Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11591/ijaas.v13.i3.pp546-555

Abstract

The idea of an addition chain can be applied to scalar multiplication involving huge number operations in elliptic curve cryptosystems. In this article, initially, we study the taxonomy of the addition chain problem to build up an understanding of the problem. We then examine the mathematics behind an optimal addition chain that includes the theoretical boundary for the upper limit and lower limit which laid the foundation for experimentation hereafter. In the following, we examine different addition chain solutions that were used to increase efficiency in scalar multiplication. To avoid any possible confusion, we intentionally separated the discussion into two modules called integer recoding method and chain generator based on the heuristics method. These methods were developed by considering various aspects such as the space within which the operation is executed, the curve that is selected, the formulation to express the original equation, and the choices of operation and arithmetic, all together to improve operational efficiency.
Co-Authors Amri Abidin, Ahmad Faisal Derahman, Mohd Noor Mamat, Abd Rasid Mohamed, Mohamad Afendee Mohd Satar, Siti Dhalila Shawai, Yahaya Garba