Elliptic curve matrices over group ring to improve elliptic curve–discrete logarithm cryptosystems

Luhaib, Qasim Mohsin; Ajeena, Ruma Kareem K.

doi:10.47974/JDMSC-1616

Open Access Research Article

Elliptic curve matrices over group ring to improve elliptic curve–discrete logarithm cryptosystems

^*Qasim Mohsin LuhaibCorresponding authorqasimmohsinluhaib@gmail.comDepartment of MathematicsCollege of Education for Pure SciencesUniversity of BabylonBabil, IraqView full profile → , Ruma Kareem K. Ajeenapure.rume.k@uobabylon.edu.iqDepartment of MathematicsCollege of Education for Pure SciencesUniversity of BabylonBabil, IraqView full profile →

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pp. 1699–1704Vol. 26Issue 6September 2023DOI: 10.47974/JDMSC-1616 Crossmark XML

Received:: 05 Mar 2022
Accepted:: 05 Apr 2022
Published Online:: 01 Jun 2023
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-1616
Pages:: 1699–1704

Abstract

An elliptic curve matrix (ECM) is created randomly based on an elliptic curve group to modify the elliptic curve-discrete logarithm (EC-DL) cryptosystems, which are elliptic Diffie-Hellman key exchange (DHKE) and elliptic ElGamal public key cryptosystem (EEPKC), and to increase the security level in comparison with the original EC-DL schemes. In proposed schemes, the keys and ciphertext are computed using the ECMs. The security of trust schemes depended on the difficulty of solving the elliptic curve discrete logarithm problem (ECM-DLP). New experimental results on proposed schemes are discussed. The ECM-DL schemes consider new insights for more secure communications.

Keywords

Elliptic curve cryptography ECMs DHKE EEPKC Security

Subject Classifications

14G5011Gxx16U60

References

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