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A Novel Dynamic Mathematical Model Applied in Hash Function Based on DNA Algorithm and Chaotic Maps

Author

Listed:
  • Nada E. El-Meligy

    (Electrical Engineering Department, Benha Faculty of Engineering, Benha University, Benha 13511, Egypt)

  • Tamer O. Diab

    (Electrical Engineering Department, Benha Faculty of Engineering, Benha University, Benha 13511, Egypt)

  • Ashraf S. Mohra

    (Electrical Engineering Department, Benha Faculty of Engineering, Benha University, Benha 13511, Egypt)

  • Ashraf Y. Hassan

    (Electrical Engineering Department, Benha Faculty of Engineering, Benha University, Benha 13511, Egypt)

  • Wageda I. El-Sobky

    (Department of Basic Engineering Sciences, Canadian International College (CIC), New Cairo 11865, Egypt
    Department of Basic Engineering Sciences, Benha Faculty of Engineering, Benha University, Benha 13511, Egypt)

Abstract

This paper aims to improve SHA-512 security without increasing complexity; therefore, we focused on hash functions depending on DNA sequences and chaotic maps. After analysis of 45 various chaotic map types, only 5 types are selected in this proposal—namely, improved logistic, cosine logistic map, logistic sine system, tent sine system, and hybrid. Using DNA features and binary coding technology with complementary rules to hide information is a key challenge. This article proposes improving SHA-512 in two aspects: the modification of original hash buffer values, and the modification of additive constants K t . This proposal is to make hash buffer values (a, b, c, d, e, f, g, and h) and K t dependent on one-dimensional discrete chaotic maps and DNA sequences instead of constant. This modification complicates the relationship between the original message and hash value, making it unexpected. The performance of the proposed hash function is tested and analyzed the confusion, diffusion, and distributive and compared with the original SHA-512. The performance of security is analyzed by collision analysis, for which the maximum number of hits is only three, showing that the proposed hash function enhances the security and robustness of SHA-512. The statistical data and experimental analysis indicate that the proposed scheme has good properties and satisfies high-performance requirements for secure hash functions.

Suggested Citation

  • Nada E. El-Meligy & Tamer O. Diab & Ashraf S. Mohra & Ashraf Y. Hassan & Wageda I. El-Sobky, 2022. "A Novel Dynamic Mathematical Model Applied in Hash Function Based on DNA Algorithm and Chaotic Maps," Mathematics, MDPI, vol. 10(8), pages 1-21, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1333-:d:795881
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    References listed on IDEAS

    as
    1. Mazloom, Sahar & Eftekhari-Moghadam, Amir Masud, 2009. "Color image encryption based on Coupled Nonlinear Chaotic Map," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1745-1754.
    2. Tongfeng Zhang & Shouliang Li & Rongjun Ge & Min Yuan & Yide Ma, 2016. "A Novel 1D Hybrid Chaotic Map-Based Image Compression and Encryption Using Compressed Sensing and Fibonacci-Lucas Transform," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-15, May.
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    Cited by:

    1. Larissa V. Cherckesova & Olga A. Safaryan & Nikita G. Lyashenko & Denis A. Korochentsev, 2022. "Developing a New Collision-Resistant Hashing Algorithm," Mathematics, MDPI, vol. 10(15), pages 1-12, August.

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