A Novel Hybrid Secure Image Encryption Based on Julia Set of Fractals and 3D Lorenz Chaotic Map
Open accessAbstract
Chaos-based encryption schemes have attracted many researchers around the world in the digital image security domain. Digital images can be secured using existing chaotic maps, multiple chaotic maps, and several other hybrid dynamic systems that enhance the non-linearity of digital images. The combined property of confusion and diffusion was introduced by Claude Shannon which can be employed for digital image security. In this paper, we proposed a novel system that is computationally less expensive and provided a higher level of security. The system is based on a shuffling process with fractals key along with three-dimensional Lorenz chaotic map. The shuffling process added the confusion property and the pixels of the standard image is shuffled. Three-dimensional Lorenz chaotic map is used for a diffusion process which distorted all pixels of the image. In the statistical security test, means square error (MSE) evaluated error value was greater than the average value of 10000 for all standard images. The value of peak signal to noise (PSNR) was 7.69(dB) for the test image. Moreover, the calculated correlation coefficient values for each direction of the encrypted images was less than zero with a number of pixel change rate (NPCR) higher than 99%. During the security test, the entropy values were more than 7.9 for each grey channel which is almost equal to the ideal value of 8 for an 8-bit system. Numerous security tests and low computational complexity tests validate the security, robustness, and real-time implementation of the presented scheme.
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The execution time of SCEC is 0.2 s, compared to 1.708 s, 4.750 s, 4.828 s, and 3.253 s for Refs [32], [33], [34], and [35], respectively.
“Ref. [32] Ref. [33] Ref. [34] Ref. [35] Time (s) 0.2 1.708 4.750 4.828 3.253”
From Cryptosystem Based on the Elliptic Curve With a High Degree of Resistance to Damage on the Encrypted Images (2020) · cites this paper as [32]
Section 6.8 (Time Complexity; page unavailable) says the authors measured their encryption scheme’s execution time and refers to Table 12, but the passages in our copy do not give the claimed 1.708 s value or the comparison times. Searches for 1.708, SCEC, and the listed times found no passage establishing those numbers. (LLM, conf=0.72)
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Image Encryption Using Lorenz Chaotic System
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“The entropy results generated by SCEC when applied to a series of well-known images surpassed the performance of other cryptosystems [30], [31].”
MethodInvestigation of the Simplest Megastable Chaotic Oscillator with Spatially Triangular Wave Damping
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- Authors
- Masood, F., Ahmad, J., Shah, S. A., Jamal, S. S., & Hussain, I.
- Affiliations
- Institute of Space Technology (PK)
- Edinburgh Napier University (GB)
- Manchester Metropolitan University (GB)
- King Khalid University (SA)
- Qatar University (QA)
- Corresponding author
- Shah, Syed Aziz
- Venue
- Entropy
- Publisher
- MDPI AG
- Published
- 2020-02-28
- Volume
- 22
- Issue
- 3
- Pages
- 274
- ISSN
- 1099-4300 (ISSN-L)
- PMC
- PMC7516729
- OpenAlex
- W3008319366
- Cited by
- 125
- References
- 85
- Citations by year
- 2026: 3 · 2025: 8 · 2024: 16 · 2023: 21 · 2022: 34 · 2021: 27 · 2020: 16
- FWCI
- 9.52
- Type
- journal article
- Language
- en
- Open access
- gold
- dx.doi.org
- Licence
- Locations
- Entropy (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- Edinburgh Napier Research Repository (Edinburgh Napier University) (publishedVersion, cc-by)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Research Output (Edinburgh Napier University) (submittedVersion, cc-by)
- Qatar University QSpace (Qatar University) (submittedVersion)
- Funders
- Deanship of Scientific research at King Khalid University (R.G.P 2/58/40)
- Topics
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Chaos-based Image/Signal Encryption
- Physical Sciences › Computer Science › Artificial Intelligence › Computer Science and Engineering
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Advanced Steganography and Watermarking Techniques
- Keywords
- image encryption, chaos-based cryptography, Julia sets, confusion and diffusion, pixel shuffling, hybrid chaotic maps, NPCR, entropy analysis
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