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All Journal International Journal of Advances in Applied Sciences Bulletin of Electrical Engineering and Informatics
Derahman, Mohd Noor
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Earth & Planetary Sciences Electrical & Electronics Engineering Environmental Science Materials Science & Nanotechnology Mathematics Physics

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Challenges in data representation for efficient execution of encryption operation Afendee Mohamed, Mohamad; Garba Shawai, Yahaya; Almaiah, Mohammed Amin; Derahman, Mohd Noor; Lutfi, Abdalwali; Abu Bakar, Khairul Azmi
Bulletin of Electrical Engineering and Informatics Vol 13, No 2: April 2024
Publisher : Institute of Advanced Engineering and Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11591/eei.v13i2.5437

Abstract

Big number operation has always been a bottleneck to computer system as it imposes high demand on computing power. With a limited power available, operations such as exponentiation and multiplication involving large integer belonging to encryption process requires grave scrutiny. One way to address this issue is by replacing an original complex computation into a sequence of small computations that in the end produces the same results. This paper takes an evolutionary approach to survey numerous articles that have contributed to the advancement of integer representation. Numerous representations were proposed, those that come into play concentrated on reducing non-zero digits and limiting non-zero spacing other than allowing subtraction operation. A comparison was made to distinguish the properties of each method from the others. This detailed outlook can be a guide for identifying the correct representation to be chosen for implementation within specific application.
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 Abdul Kadir, Mohd Fadzil Abu Bakar, Khairul Azmi Afendee Mohamed, Mohamad Almaiah, Mohammed Amin Amri Abidin, Ahmad Faisal Garba Shawai, Yahaya Lutfi, Abdalwali Mamat, Abd Rasid Mohamed, Mohamad Afendee Mohd Satar, Siti Dhalila Shawai, Yahaya Garba