Key Generation Technique based on Triangular Coordinate Extraction for Hybrid Cubes

Muhammad Faheem Mushtaq, Sapiee Jamel, Kamaruddin Malik Mohamad, Shamsul Kamal Ahmad Khalid, Mustafa Mat Deris


Cryptographic algorithms play an important role in information security where it ensures the security of data across the network or storage. The generation of Hybrid Cubes (HC) based on permutation and combination of integer numbers are utilized in the construction of encryption and decryption key in the non-binary block cipher. In this study, we extend the hybrid cube encryption algorithm (HiSea) and our earlier Triangular Coordinate Extraction (TCE) technique for HC by increasing the complexity in the mathematical approaches. We proposed a new key generation technique based on TCE for the security of data. In this regard, the Hybrid Cube surface (HCs) is divided into four quarters by the intersection of primary and secondary diagonal and each quarter is rotated by using the rotation points. The overall security of HC is improved by the rotation of HCs and enhanced the complexity in the design of key schedule algorithm. The brute force and entropy test are applied in experimental results which proved that the proposed technique is suitable for implementing a key generation technique and free from any predicted keys pattern.


Cryptographic Algorithms; Hybrid Cubes; Key Generation Technique; Non-Binary Block Cipher;

Full Text:



N. Kumar and P. Chaudhary, “Performance evaluation of encryption/decryption mechanisms to enhance data security,” Indian Journal of Science and Technology, vol. 9, no. 20, 2016.

M. Ebrahim, S. Khan, and U. Bin Khalid, “Symmetric Algorithm Survey: A Comparative Analysis,” International Journal of Computer Applications, vol. 61, no. 20, pp. 12–19, 2013.

Disina, A. H., Pindar, Z. A., & Jamel, S., “Enhanced Caeser Cipher to Exclude Repetition and Withstand Frequency Cryptanalysis,” In Proceedings of the International Conference on Information Science and Security (ICISS), 2015.

S. H. Jamel and M. M. Deris, “Diffusive primitives in the design of modern cryptographic algorithms,” in Proceedings of the International Conference on Computer and Communication Engineering, 2008, pp. 707–710.

National Institute of Standards (NIST), Federal Information Processing Standards Publication197: Advanced encryption standard (AES). 2001.

R. R. Rachh, P. V. A. Mohan, and B. S. Anami, “Implementation of AES Key Schedule Using Look-Ahead Technique,” Circuits, Systems, and Signal Processing, vol. 33, no. 11, pp. 3663–3670, 2014.

A. H. Disina, S. Jamel, Z. A. Pindar, and M. M. Deris, “All-or-nothing Key Derivation Function Based on Quasigroup String,” in Proceedings of the International Conference on Information Science and Security (ICISS), 2016, pp. 6–10.

M. Trenkler, “An algorithm for making magic cubes,” The Pi ME Journal, vol. 12, no. 2, pp. 105–106, 2005.

L. Zhang, X. Tian, and S. Xia, “Scrambling algorithm of image encryption based on Rubik’s cube rotation and logistic sequence,” in Proceedings of the International Conference on Multimedia and Signal Processing, CMSP, 2011, vol. 1, pp. 312–315.

B. Nini and D. Bouteldja, “Virtual Cylindrical View of a Color Image for its Permutation for an Encryption Purpose,” International Journal of Computer Applications, vol. 16, no. 1, pp. 11–17, 2011.

J. Shen, X. Jin, and C. Zhou, “A color image encryption algorithm based on magic cube transformation and modular arithmetic operation,” Advances in Multimedia Information Processing, vol. 3768, pp. 270–280, 2005.

L. Zhang, S. Ji, Y. Xie, Q. Yuan, Y. Wan, and G. Bao, “Principle of image encrypting algorithm based on magic cube transformation,” Computational Intelligence and Security, vol. 3802, pp. 977–982, 2005.

Q. Wu, C. Zhu, J. J. Li, C. C. Chang, and Z. H. Wang, “A magic cube based information hiding scheme,” Journal of information security and application, vol. 26, pp. 1–7, 2016.

S. Jamel, T. Herawan, and M. M. Deris, “A cryptographic algorithm based on hybrid cubes,” Computational Science and Its Applications ICCSA, vol. 6019, pp. 175–187, 2010.

S. Jamel, M. M. Deris, I. T. R. Yanto, and T. Herawan, “The hybrid cubes encryption algorithm (HiSea),” Communications in Computer and Information Science, vol. 154, pp. 191–200, 2011.

D. Rajavel and S. P. Shantharajah, “Cryptography Based on Combination of Hybridization and Cube’s Rotation,” International Journal of Computational Intelligence and Informatics, vol. 1, no. 4, pp. 294–299, 2012.

P. R. Kumar, S.S.Dhenakaran, K.L.Sailaja, and P.SaiKishore, “CHAKRA: A New Approach for Symmetric Key Encryption,” in Proceedings of the 2012 World Congress on Information and Communication Technologies, WICT, 2012, pp. 727–732.

N. Anghel, “Determinant Identities and the Geometry of Lines and Circles,” The Journal of Ovidius University of Constanta, Versita, vol. 22, pp. 37–49, 2014.

M. F. Mushtaq, S. Jamel, and M. M. Deris, “Triangular Coordinate Extraction (TCE) for Hybrid Cubes,” Journal of Engineering and Applied Sciences, vol. 12, no. 8, pp. 2164-2169, 2017.

D. Hearn and M. P. Baker, Computer Graphics - C version. Pearson Education, 2005.

E. B. Barker and A. Roginsky, “Recommendation for Cryptographic Key Generation,” NIST Special Publication 800-133, pp. 1–26, 2012.

L. May, M. Henricksen, W. Millan, G. Carter, and E. Dawson, “Strengthening the Key Schedule of the AES,” in Proceedings of the 7th Australian Conference on Information Security and Privacy, 2002, pp. 226–240.

S. Jamel, The Hybrid Cubes Encryption Algorithm (HiSea). Ph.D Thesis, University Tun Hussein Onn Malaysia (UTHM), Johor, Malaysia, pp. 1–138, 2012.


  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.

ISSN: 2180-1843

eISSN: 2289-8131