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Cited by 155Chaos-based Image/Signal EncryptionQuantum Information and CryptographyCellular Automata and Applications

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Quantum-inspired cascaded discrete-time quantum walks with induced chaotic dynamics and cryptographic applications

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Abd El-Latif, Ahmed A., Abd-El-Atty, Bassem, Amin, Mohamed, Iliyasu, Abdullah M.·2020·Scientific Reports
DOI 10.1038/s41598-020-58636-wPMC PMC7005306
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Abstract

Designing efficient and secure cryptosystems has been a preoccupation for many scientists and engineers for a long time wherein they use chaotic systems to design new cryptosystems. While one dimensional (1-D) chaotic maps possess powerful properties compared to higher dimension ones, they are vulnerable to various attacks due to their small key space, chaotic discontinuous ranges, and degradation in chaotic dynamical behaviours. Moreover, when simulated on a computer, every such chaotic system produces a periodic cycle. Meanwhile, quantum random walks exhibit the potential for deployment in efficient cryptosystem design, which makes it an excellent solution for this problem. In this context, we present a new method for constructing substitution boxes (S-boxes) based on cascaded quantum-inspired quantum walks and chaos inducement. The performance of the proposed S-box scheme is investigated via established S-box evaluation criterion and outcomes suggest that the constructed S-box has significant qualities for viable applications information security. Further, we present an efficient scheme for pseudo-random numbers generation (PRNG) whose sustainability over long periods remedies the periodicity problem associated with traditional cryptographic applications. Furthermore, by combining the two mechanisms, an atypical image encryption scheme is introduced. Simulation results and analysis validate that the proposed image encryption algorithm will offer gains in many cryptographic applications.

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Crossref · 10.1038/s41598-020-58636-w

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Figures

Figure 1 Outline of the proposed PRNG sequence generation mechanism.
Figure 1 Outline of the proposed PRNG sequence generation mechanism.CC BY · PubMed Central
Algorithm 1 Image encryption algorithm.
Algorithm 1 Image encryption algorithm.CC BY · PubMed Central
Figure 2 General framework for the proposed image encryption technique.
Figure 2 General framework for the proposed image encryption technique.CC BY · PubMed Central
Figure 3 Test images (a–f), their encrypted (in (g–l)), and decrypted (in (m–r)) versions.
Figure 3 Test images (a–f), their encrypted (in (g–l)), and decrypted (in (m–r)) versions.CC BY · PubMed Central
Figure 4 Correlation distribution for neighbouring pixel pairs along horizontal, vertical and diagonal directions for Bridge image in Fig. 3(a).
Figure 4 Correlation distribution for neighbouring pixel pairs along horizontal, vertical and diagonal directions for Bridge image in Fig. 3(a).CC BY · PubMed Central
Figure 5 Correlation distribution for neighbouring pixel pairs along horizontal, vertical and diagonal directions for red channel of Sailboat image in Fig. 3(d).
Figure 5 Correlation distribution for neighbouring pixel pairs along horizontal, vertical and diagonal directions for red channel of Sailboat image in Fig. 3(d).CC BY · PubMed Central
Figure 6 Correlation distribution for neighbouring pixel pairs along horizontal, vertical and diagonal directions for green channel of Sailboat image in Fig. 3(d).
Figure 6 Correlation distribution for neighbouring pixel pairs along horizontal, vertical and diagonal directions for green channel of Sailboat image in Fig. 3(d).CC BY · PubMed Central
Figure 7 Correlation distribution for neighbouring pixel pairs along horizontal, vertical and diagonal directions for blue channel of Sailboat image in Fig. 3(d).
Figure 7 Correlation distribution for neighbouring pixel pairs along horizontal, vertical and diagonal directions for blue channel of Sailboat image in Fig. 3(d).CC BY · PubMed Central
Figure 8 Histograms of original and encrypted greyscale images (in Fig. 3(a–c)).
Figure 8 Histograms of original and encrypted greyscale images (in Fig. 3(a–c)).CC BY · PubMed Central
Figure 9 Histograms of original and encrypted R, G, and B channels of the Sailboat image (in Fig. 3(d)).
Figure 9 Histograms of original and encrypted R, G, and B channels of the Sailboat image (in Fig. 3(d)).CC BY · PubMed Central
Figure 10 Decrypted Bridge image (in Fig. 3(g)) for several S-box keys.
Figure 10 Decrypted Bridge image (in Fig. 3(g)) for several S-box keys.CC BY · PubMed Central
Figure 11 Decrypted Sailboat image for several PRNG keys.
Figure 11 Decrypted Sailboat image for several PRNG keys.CC BY · PubMed Central
Figure 12 Probability distribution for running two-walker quantum walks on a circle with 11 vertices for 51 steps, where the initial coin particles are Hc1=|0〉 and Hc2=|1〉. Here, it is deducible that for a circle with only odd v nodes, the probability has nonzero in any position if the number of steps t is greater than the number of nodes v.
Figure 12 Probability distribution for running two-walker quantum walks on a circle with 11 vertices for 51 steps, where the initial coin particles are Hc1=|0〉 and Hc2=|1〉. Here, it is deducible that for a circle with only odd v nodes, the probability has nonzero in any position if the number of steps t is greater than the number of nodes v.CC BY · PubMed Central

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Citations

Cites

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Cited by

Sorted by citations

  • Providing End-to-End Security Using Quantum Walks in IoT Networks

    El-Latif, A. A. A., Abd-El-Atty, B., Venegas-Andraca, S. E., Elwahsh, H., Piran, M. J., Bashir, A. K., Song, O.-Y., & Mazurczyk, W. (2020) · IEEE Access · doi:10.1109/access.2020.2992820 · Cited by 89

    “However, the implementation of two-walker QW requires more physical resources than the realization of one-walker QW [41], that is why consequently Abd-El-Atty et al [36] designed a quantum encryption approach based on controlled one-walker QW. Finally, El-Latif et al [37] presented an image encryption approach using c…”
    BackgroundSelf-citation

  • Bijective S-Boxes Method Using Improved Chaotic Map-Based Heuristic Search and Algebraic Group Structures

    Ahmad, M., Al-Solami, E., Alghamdi, A. M., & Yousaf, M. A. (2020) · IEEE Access · doi:10.1109/access.2020.3001868 · Cited by 71

    “For our S-box, the imbalance on the input/output EX-OR distribution is calculated as differential probability whose maximum value is 0.04687 which is capable to resist the differential cryptanalysis in better as compared to the S-boxes found in [22], [74], [82] and comparable to other findings.”
    BackgroundResultInfluential

Metadata

Authors
Abd El-Latif, A. A., Abd-El-Atty, B., Amin, M., & Iliyasu, A. M.
Affiliations
  • Menoufia University (EG)
  • Changchun University of Science and Technology (CN)
Corresponding author
  • Abd-El-Atty, Bassem
  • Iliyasu, Abdullah M.
ORCID
Venue
Scientific Reports
Publisher
Springer Science and Business Media LLC
Published
2020-02-06
Volume
10
Issue
1
Pages
1930-1930
ISSN
2045-2322 (ISSN-L)
DOI
10.1038/s41598-020-58636-w
PMC
PMC7005306
OpenAlex
W3005238411
Cited by
155
References
3
Citations by year
2026: 4 · 2025: 19 · 2024: 24 · 2023: 23 · 2022: 36 · 2021: 36 · 2020: 13
FWCI
10.50
Type
journal article
Language
en
Open access
Licence
Locations
  • Scientific Reports (publishedVersion, cc-by)
  • Europe PMC (PubMed Central) (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
  • Greater South Information System
Funders
  • Prince Sattam bin Abdulaziz University (2019/01/9862)
  • Menofia University
Topics
  • Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Chaos-based Image/Signal Encryption
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Cellular Automata and Applications
Keywords
discrete-time quantum walks, chaotic maps, substitution boxes, S-box design, pseudorandom number generation, image encryption, quantum cryptography, chaotic dynamics

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