Cryptosystems based on the Edward curve scalar multiplication matrix function

Aljamaly, Karrar Taher R.; Hassan, Zainab Flaih; Naji, Sadeq Hamdallah

doi:10.47974/JDMSC-2673

Open Access Research Article

Cryptosystems based on the Edward curve scalar multiplication matrix function

^*Karrar Taher R. AljamalyCorresponding authorkarrar.taher@ec.edu.iqDepartment of MathematicsNajaf Study CenterOpen Educational CollegeNajaf, Iraq0000-0001-8447-3865View full profile → , Zainab Flaih HassanZainab.flaih@ec.edu.iqDepartment of MathematicsNajaf Study CenterOpen Educational CollegeNajaf, Iraq0000-0001-7254-6668View full profile → , Sadeq Hamdallah Najialhsynawysadq278@gmail.comDepartment of MathematicsNajaf Study CenterOpen Educational CollegeNajaf, IraqView full profile →

* Corresponding author · click or hover a name for details

pp. 2035–2040Vol. 29Issue 5May 2026DOI: 10.47974/JDMSC-2673 Crossmark XML

Received:: 01 Nov 2025
Published Online:: 22 May 2026
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-2673
Pages:: 2035–2040

Abstract

The key point in this paper is the definition of new mathematical concepts based on point doubling and addition on the Edward curve group and matrix power functions. The basic idea is known as the Edward scalar multiplication matrix function (E_dSMMF). Also proposed is a modification to the Diffie-Hellman and ElGamal schemes in the Edward curve cryptosystem, which is more secure than the original because the discrete logarithm problem is computationally infeasible to solve.

Keywords

Edward curve cryptography Scalar multiplication matrix function Diffie – hellman key exchange ElGamal public key cryptosystem

Subject Classifications

Primary 93A30Secondary 49K15

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