Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2025 Jul 1;15(1):22206.
doi: 10.1038/s41598-025-04700-2.

Secure data transmission through fractal-based cryptosystem: a Noor iteration approach

Deepak Negi  1 , Rajiv Kumar  2 , Vijay Kumar  3 , Arvind Dhaka  4
Affiliations

Secure data transmission through fractal-based cryptosystem: a Noor iteration approach

Deepak Negi et al. Sci Rep. .

Abstract

The data must be protected from cyber-attacks that benefit from the weaknesses of the databases. Our traditional techniques are unstable. They are not strong enough to withstand the sophisticated and advanced criminal methods that attackers are developing and using to access confidential information. To prevent these kinds of activities, we must use encryption techniques. The most common Brute force encryption method, which can easily break encryption that is not very strong, is one of the many encryption and decryption techniques used by cyber attackers to break unsafe techniques during data transformation over a network. This paper addresses these challenges and provides a strong and effective encryption technique. Fractals are indefinite parameters and functions that can be used to enhance encryption techniques, and one of them we used in our study was to optimize the encryption technique. In this paper, we introduced a new and reliable encryption technique that utilizes the chaotic and fractal nature of Noor iteration. Our study intends to improve real-time protection against new attack vectors. The proposed approach ensures key sensitivity by generating an initial value set throughout the Noor iteration process. Initial Key values are produced by the fractal function using the Julia set and the XOR operator. Our study shows the efficiency, reliability, and potential for secure communications. The sequence encrypts the plain text, and the entire process is evaluated using analysis that includes key space, sensitivity, differential, and statistical evaluations.

Keywords: Cyber theft; Data communication; Fractal cryptosystem; Iterative functions; Noor orbit.

PubMed Disclaimer

Conflict of interest statement

Declarations. Competing interests: The authors declare no conflict of interest.

Figures

Fig. 1
Fig. 1
Mandelbrot Set and related images of Julia Sets.
Fig. 2
Fig. 2
Encryption (a) and decryption (b) mechanisms use public keys generated by the sender and the receiver.
Fig. 3
Fig. 3
Julia set for formula image, formula image, formula image.
Fig. 4
Fig. 4
3-D chart of the encrypted message.
Fig. 5
Fig. 5
Chart of the encrypted message.
See this image and copyright information in PMC

References

    1. Agarwal, S. Secure image transmission using fractal and 2D-chaotic map. J. Imaging4(1), 17 (2018).
    1. Ahmad, M. et al. An image encryption algorithm based on new generalized fusion fractal structure. Inf. Sci.592, 1–20 (2022).
    1. Agarwal, S. A fractal based image cipher using Knuth shuffle method and dynamic diffusion. IJCNC11, 81–100 (2019).
    1. Alia, M. A. & Suwais, K. Improved steganography scheme based on fractal set. Int. Arab J. Inf. Technol.17(1), 128–136 (2020).
    1. Ayubi, P., Setayeshi, S. & Rahmani, A. M. Deterministic chaos game: a new fractal based pseudo-random number generator and its cryptographic application. J. Inf. Secur. Appl.52, 102472 (2020).

LinkOut - more resources