Skip to main content
SpringerLink
Log in

Piecewise symmetric magic cube: application to text cryptography

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

Abstract

This article propounds a Piecewise Symmetric Magic Cube (PSMC), the properties of which have reinvigorated its application to text encryption. A method has been introduced for the construction of magic cubes of order m × 2l, for all \(l,m (m {\text {even}})\in N\cup \left \lbrace 0 \right \rbrace , m\geq 4\) by using the concept of compounding. The behavior of elements in PSMC is controlled by the starting variables (Sstart and Lstart). The formula for evaluation of the magic sum of these magic cubes have been derived, which ensures magic nature of PSMC. Additionally, PSMC are applied to the field of text cryptography. The proposed text encryption model is applicable for the encryption and decryption of any language that may include numeric digits, and special characters along with their different combinations. Also, the validation of this model has been checked by focusing on the analysis of bilingual data (English-German, English-Hindi, German-Hindi, French-Arabic, and Italian-Spanish). The performance evaluation metrices (brute-force analysis, avalanche effect, CPU time analysis, Shannon entropy, and known plain text analysis) have been carried to analyze the resisting efficiency of the proposed model against different types of attacks. An analysis of encryption/ decryption time shows that decryption is more time-efficient which protects the data from getting being corrupted by the intruders. The distinct entries of PSMC remove the problem of repetition in cipher text which raises the level of security to a higher extent.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Algorithm 1
Algorithm 2
Algorithm 3
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Alspach B, Heinrich K (1981) Perfect magic cubes of order 4m. Fibonacci Quarterly 19:97–106

    MathSciNet  MATH  Google Scholar 

  2. Alvarez G, Li S (2006) Some basic cryptographic requirements for chaos-based cryptosystems. Int J Bifurcation Chaos 16(08):2129–2151

    Article  MathSciNet  MATH  Google Scholar 

  3. Andrew W (1960) Magic Square and Cubes-Second edition. Dover Publications, New York

    Google Scholar 

  4. Arroyo J C T, Dumdumaya C E, Delima A J P (2020) Polybius square in cryptography: a brief review of literature. Int J Adv Trends Comput Sci Eng 9(3):3798–3808

    Article  Google Scholar 

  5. Bajaj N (2022) Caesar cipher. The MathWorks, USA

    Google Scholar 

  6. Bharathi B, Manivasagam G, Kumar M A (2017) Metrics for performance evaluation of encryption algorithms. Int J Adv Res Sci Eng 6(3):62–72

    Google Scholar 

  7. Bouffard F (2022) Rot13. The MathWorks, USA

    Google Scholar 

  8. Chen X. -s. (2002) Ways of constructing optimal magic cube of order n when (n, 2· 3· 5· 7)= 1. J Central South University of Technology 9(1):70–72

    Article  Google Scholar 

  9. Chiron L, Oger G, De Leffe M, Le Touzé D (2018) Analysis and improvements of adaptive particle refinement (apr) through cpu time, accuracy and robustness considerations. J Comput Phys 354:552–575

    Article  MathSciNet  MATH  Google Scholar 

  10. Dawood O (2015) Development of symmetric cryptographic models and asymmetric models based on magic cube. University of Technology, Iraq, Ph.D. thesis

  11. Galar D, Kumar U (2017) Chapter 3 - preprocessing and features. In: eMaintenance. Academic Press, pp 129–177

  12. George D, Geetha J S, Mani K (2014) Add-on security level for public key cryptosystem using magic rectangle with column/row shifting. Int J Comput Appl 975(8887):38–43

    Google Scholar 

  13. Gustafson H, Dawson E, Nielsen L, Caelli W (1994) A computer package for measuring the strength of encryption algorithms. Comput Security 13 (8):687–697

    Article  Google Scholar 

  14. Hankerson D, Menezes AJ, Vanstone S (2006) Guide to elliptic curve cryptography. Springer Science & Business Media

  15. Hill D (2022) Advanced encryption standard (aes)-128,192, 256. The MathWorks Natick, USA

    Google Scholar 

  16. Jamel S, Herawan T, Deris MM (2010) A cryptographic algorithm based on hybrid cubes. In: International conference on computational science and its applications. Springer, vol 6019, pp 175–187

  17. Jiang Y, Susilo W, Mu Y, Guo F (2018a) Ciphertext-policy attribute-based encryption supporting access policy update and its extension with preserved attributes. Int J Inf Secur 17(5):533–548

    Article  Google Scholar 

  18. Jiang Y, Susilo W, Mu Y, Guo F (2018b) Flexible ciphertext-policy attribute-based encryption supporting and-gate and threshold with short ciphertexts. Int J Inf Secur 17(4):463–475

    Article  Google Scholar 

  19. Khanas Y, Borecki M (2020) Research on the use of algorithms for matrix transformations for encrypting text information. Security and Privacy 3 (6):e108

    Article  Google Scholar 

  20. Krishna G J, Ravi V, Bhattu S N (2018) Key generation for plain text in stream cipher via bi-objective evolutionary computing. Appl Soft Comput 70:301–317

    Article  Google Scholar 

  21. Kumar A, Tiwari N (2012) Effective implementation and avalanche effect of aes. International Journal of Security. Privacy Trust Management (IJSPTM) 1(3/4):31–35

    Google Scholar 

  22. Lee S, Kim S, Jung K (2013) A symmetric key cryptography algorithm by using 3-dimensional matrix of magic squares. In: Proceedings of the Korea information processing society conference. Korea Information Processing Society, vol 20, pp 768–770

  23. Lin K Y (1986) Magic cubes and hypercubes of order 3. Discrete mathematics 58(2):159–166

    Article  MathSciNet  MATH  Google Scholar 

  24. Mani K, Viswambari M (2017) Enhancing the security in cryptosystems based on magic rectangle. Int J Comput Netw Inform Sec, vol 9(4)

  25. Michel R, Taubenfeld G, Berman A (1995) A connection between random variables and latin k-cubes. Discret Math 146(1-3):313–320

    Article  MathSciNet  MATH  Google Scholar 

  26. Mushtaq M F, Jamel S, Radhiah S, Akram U, Mat M (2019) Key schedule algorithm using 3-dimensional hybrid cubes for block cipher. Int J Adv Comput Sci Appl 10(8):427–442

    Google Scholar 

  27. National Academies of Sciences, Medicine E et al (2018) Decrypting the Encryption Debate: A Framework for Decision Makers. National Academies Press, Washington

    Google Scholar 

  28. Nordgren R P (2012) On properties of special magic square matrices. Linear Algebra Appl 437(8):2009–2025

    Article  MathSciNet  MATH  Google Scholar 

  29. Pavithran P, Mathew S, Namasudra S, Srivastava G (2022) A novel cryptosystem based on dna cryptography, hyperchaotic systems and a randomly generated moore machine for cyber physical systems. Comput Commun 188:1–12

    Article  Google Scholar 

  30. Rajavel D, Shantharajah S (2012) Cubical key generation and encryption algorithm based on hybrid cube’s rotation. In: International conference on pattern recognition, informatics and medical engineering (PRIME-2012). IEEE, pp 183–187

  31. Rani N, Mishra V (2022) Behavior of powers of odd ordered special circulant magic squares. Int J Math Educ Sci Technol 53(4):1044–1062

    Article  MATH  Google Scholar 

  32. Rasmi P, Paul V (2014) An efficient mixed mode and paired cipher text cryptographic algorithm for effective key distribution. Int J Commun Syst 11(27):2593–2603

    Google Scholar 

  33. Richards D (1980) Generalized magic cubes. Math Mag 53(2):101–105

    Article  MathSciNet  MATH  Google Scholar 

  34. Sef Y (2022) Feistel text encryption. The MathWorks Natick, USA

    Google Scholar 

  35. Shibiraj N, Tomba I (2018) Modified hill cipher: secure technique using latin square and magic square. Int J Comput Sci Eng 6(12):315–320

    Google Scholar 

  36. Trenkler M (2000) A construction of magic cubes. Math Gaz 84 (499):36–41

    Article  Google Scholar 

  37. Uko L U, Barron T L (2018) A generalization of trenkler’s magic cubes formula. Recreat Math Mag 4(8):39–45

    MathSciNet  Google Scholar 

  38. Xu J, Zhou J (2021) Strong leakage-resilient encryption: enhancing data confidentiality by hiding partial ciphertext. Int J Inf Secur 20(2):141–159

    Article  MathSciNet  Google Scholar 

  39. Yuan Y, Mo Y (2020) Security for cyber-physical systems: Secure control against known-plaintext attack. Sci China Technol Sci 63(9):1637–1646

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, Sangrur, 148106, Punjab, India

    Narbda Rani & Vinod Mishra

  2. Department of Computer Science and Engineering, Sant Longowal Institute of Engineering and Technology, Longowal, Sangrur, 148106, Punjab, India

    Birmohan Singh

Authors
  1. Narbda Rani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vinod Mishra
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Birmohan Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Narbda Rani.

Ethics declarations

Conflict of Interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rani, N., Mishra, V. & Singh, B. Piecewise symmetric magic cube: application to text cryptography. Multimed Tools Appl 82, 19369–19391 (2023). https://doi.org/10.1007/s11042-022-14153-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-022-14153-8

Keywords

Search

Navigation