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Pseudo random sequences based on elliptic curve subgroups and mathematical model for its application to digital image security

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Abstract

The security strength of the elliptic curve cryptosystems (ECC) is due to its core operations-based group law. This aspect of the elliptic curve provides key service to ensure security against modern cryptanalysis. However, the excess use of group law in EC based algorithms make it computationally hard for real time applications. In this context, this paper presented a smart-like algorithm based on subgroup co-set operations. The suggested scheme uses all co-sets that generates multiple sequences that can smoothly be adopted in most promising communication architectures of the future such as internet of things (IoT). Besides, the subgroup structure on a small prime with possible embedding is managed to construct efficient substitution box (S-box). Whereas, the performance of the proposed S-box is examined via standardized tests thus found significant for multimedia data security applications. Moreover, a small prime based EC subgroup coset model is designed, that generates a set of experimentally verified independent pseudo random streams. The atypical mathematical model for its application to image data encryption is established, by combining the S-box module (SM) and subgroup coset module (ES-PM). Several statistical tests revealed that the proposed technique is suitable for various cryptographic applications.

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Authors and Affiliations

  1. Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan

    Muhammad Imran Haider, Tariq Shah, Asif Ali, Dawood Shah & Ijaz Khalid

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  1. Muhammad Imran Haider
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  2. Tariq Shah
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  4. Dawood Shah
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Correspondence to Muhammad Imran Haider.

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Haider, M.I., Shah, T., Ali, A. et al. Pseudo random sequences based on elliptic curve subgroups and mathematical model for its application to digital image security. Multimed Tools Appl 81, 23709–23734 (2022). https://doi.org/10.1007/s11042-022-12358-5

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