TARU PUBLICATIONS
Journal of Discrete Mathematical Sciences and Cryptography cover
Hybrid ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

Association schemes in encrypting two dimensional data

* , ,

* Corresponding author · click or hover a name for details

pp. 161–183Vol. 28Issue 1February 2025DOI: 10.47974/JDMSC-2118 Crossmark XML
Received:
09 Jan 2024
Published Online:
28 Feb 2025
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2118
Pages:
161–183

Abstract

A new Crypto-Stegano system is proposed using Random Matrix Transformation on relations of association schemes based on finite abelian groups associated with Arnold tranform and concealing the encrypted data within a randomly selected cover image. The proposed technique has been evaluated through comprehensive experimental results. Additionally, statistical tools are used to assess its performance. Furthermore, error analysis and key analysis have been carried out to ensure the technique’s accuracy and reliability. Comparison results between existing schemes and the proposed techniques to validate the robustness have also been provided.

Keywords

Subject Classifications

05E3011T71

References

[1] A. A. Abdulla, H. Sellahewa, and S. A. Jassim, “Improving embedding efficiency for digital steganography by exploiting similarities between secret and cover images,” Multimedia Tools and Applications, vol. 78, no. 13, pp. 17799–17823 (2019).
[2] A. A. Abdulla, H. Sellahewa, and S. A. Jassim, “Steganography based on pixel intensity value decomposition,” in Mobile Multimedia/Image Processing, Security, and Applications 2014, vol. 9120, pp. 19–27 (2014).
[3] A. A. Abdulla, Exploiting similarities between secret and cover images for improved embedding efficiency and security in digital steganography, Ph.D. dissertation (2015).
[4] M. R. Abuturab, “Securing color information using Arnold transform in gyrator transform domain,” Optics and Lasers in Engineering, vol. 50, no. 5, pp. 772–779 (2012).
[5] V. I. Arnold and A. Avez, Ergodic Problems of Classical Mechanics, vol. 9, Benjamin (1968).
[6] A. Arora and R. K. Sharma, “Cryptanalysis and enhancement of image encryption scheme based on word-oriented feedback shift register,” Multimedia Tools and Applications, vol. 81, no. 12, pp. 16679–16705 (2022).
[7] J. Bai, C.-C. Chang, T.-S. Nguyen, C. Zhu, and Y. Liu, “A high payload steganographic algorithm based on edge detection,” Displays, vol. 46, pp. 42–51 (2017).
[8] J. Balkrishan and A. P. Singh, “Concealing data in a digital image with multilayer security,” Multimedia Tools and Applications, vol. 75, no. 12, pp. 7045–7063 (2016).
[9] J. Bao and Q. Yang, “Period of the discrete Arnold cat map and general cat map,” Nonlinear Dynamics, vol. 70, no. 2, pp. 1365–1375 (2012).
[10] R. C. Bose and T. Shimamoto, “Classification and analysis of partially balanced incomplete block designs with two associate classes,” Journal of the American Statistical Association, vol. 47, no. 258, pp. 151–184 (1952).
[11] H. Chen, X. Du, Z. Liu, and C. Yang, “Optical color image hiding scheme by using Gerchberg–Saxton algorithm in fractional Fourier domain,” Optics and Lasers in Engineering, vol. 66, pp. 144–151 (2015).
[12] L. Chen and D. Zhao, “Color image encoding in dual fractional Fourier wavelet domain with random phases,” Optics Communications, vol. 282, no. 17, pp. 3433–3438 (2009).
[13] F. J. Dyson and H. Falk, “Period of a discrete cat mapping,” The American Mathematical Monthly, vol. 99, no. 7, pp. 603–614 (1992).
[14] J.-B. Feng, H.-C. Wu, C.-S. Tsai, Y.-F. Chang, and Y.-P. Chu, “Visual secret sharing for multiple secrets,” Pattern Recognition, vol. 41, no. 12, pp. 3572–3581 (2008).
[15] U. Hayat and N. A. Azam, “A novel image encryption scheme based on an elliptic curve,” Signal Processing, vol. 155, pp. 391–402 (2019).
[16] C. Kim, D. Shin, L. Leng, and C.-N. Yang, “Separable reversible data hiding in encrypted halftone image,” Displays, vol. 55, pp. 71–79 (2018).
[17] C. Kim, C.-N. Yang, and L. Leng, “High-capacity data hiding for ABTC-EQ based compressed image,” Electronics, vol. 9, no. 4, p. 644 (2020).
[18] M. Kumar, D. C. Mishra, and R. K. Sharma, “A first approach on an RGB image encryption,” Optics and Lasers in Engineering, vol. 52, pp. 27–34 (2014).
[19] Z. Liu, Q. Guo, L. Xu, M. A. Ahmad, and S. Liu, “Double image encryption by using iterative random binary encoding in gyrator domains,” Optics Express, vol. 18, no. 11, pp. 12033–12043 (2010).
[20] Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and colorblend operation in discrete cosine transform domains,” Optics Communications, vol. 284, no. 1, pp. 123–128 (2011).
[21] Y. Luo, J. Yu, W. Lai, and L. Liu, “A novel chaotic image encryption algorithm based on improved baker map and logistic map,” Multimedia Tools and Applications, vol. 78, no. 15, pp. 22023–22043 (2019).
[22] G. Meriem and S. Bouroubi, “A new ideal secret sharing scheme based on a tree,” Journal of Discrete Mathematical Sciences and Cryptography, pp. 1–18 (2021).
[23] D. C. Mishra, H. Sharma, R. K. Sharma, and N. Kumar, “A first cryptosystem for security of two-dimensional data,” Fractals, vol. 25, no. 01, p. 1750011 (2017).
[24] D. C. Mishra, R. K. Sharma, M. Kumar, and K. Kumar, “Security of color image data designed by public-key cryptosystem associated with 2D-DWT,” Fractals, vol. 22, no. 04, p. 1450011 (2014).
[25] A. Sabharwal and P. Yadav, “Association schemes over some finite group rings,” in Mathematical Modeling, Computational Intelligence Techniques and Renewable Energy, pp. 13–23 (2022).
[26] A. Sabharwal, P. Yadav, and R. K. Sharma, “Association schemes for some finite group rings II,” Communications on Applied Nonlinear Analysis (2024).
[27] H. Sharma, D. C. Mishra, R. K. Sharma, and N. Kumar, “Multi-image steganography and authentication using crypto-stego techniques,” Multimedia Tools and Applications, vol. 80, no. 19, pp. 29067–29093 (2021).
[28] H. Sharma, D. C. Mishra, R. K. Sharma, and N. Kumar, “Crypto-stego system for securing text and image data,” International Journal of Image and Graphics, vol. 18, no. 04, p. 1850020 (2018).
[29] S. Sun, “A novel edge-based image steganography with 2k correction and Huffman encoding,” Information Processing Letters, vol. 116, no. 2, pp. 93–99 (2016).
[30] M. Tang, J. Hu, and W. Song, “A high capacity image steganography using multi-layer embedding,” Optik, vol. 125, no. 15, pp. 3972–3976 (2014).
[31] C.-N. Yang, J.-F. Ouyang, and L. Harn, “Steganography and authentication in image sharing without parity bits,” Optics Communications, vol. 285, no. 7, pp. 1725–1735 (2012).
[32] P.-H. Zieschang, An Algebraic Approach to Association Schemes, Springer (2006).

Views: 172Downloads: 67Citations: 0