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On Some Novel Results about Split-Complex Numbers, the Diagonalization Problem, and Applications to Public Key Asymmetric Cryptography

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  • Mehmet Merkepci
  • Mohammad Abobala
  • Predrag S. Stanimirović

Abstract

In this paper, we present some of the foundational concepts of split-complex number theory such as split-complex divison, gcd, and congruencies. Also, we prove that Euler’s theorem is still true in the case of split-complex integers, and we use this theorem to present a split-complex version of the RSA algorithm which is harder to be broken than the classical version. On the other hand, we study some algebraic properties of split-complex matrices, where we present the formula of computing the exponent of a split-complex matrix eX with a novel algorithm to represent a split-complex matrix X by a split-complex diagonal matrix, which is known as the diagonalization problem. In addition, many examples were illustrated to clarify the validity of our work.

Suggested Citation

  • Mehmet Merkepci & Mohammad Abobala & Predrag S. Stanimirović, 2023. "On Some Novel Results about Split-Complex Numbers, the Diagonalization Problem, and Applications to Public Key Asymmetric Cryptography," Journal of Mathematics, Hindawi, vol. 2023, pages 1-12, July.
    • Handle: RePEc:hin:jjmath:4481016
    DOI: 10.1155/2023/4481016
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