Crypto Algorithm for Binary Numbers using Knapsack via Bezier curve

Authors

  • Adil AL-Rammahi University of Kufa
  • Baleegh Alshaeer

DOI:

https://doi.org/10.31642/JoKMC/2018/120103

Keywords:

Binary numbe , Knapsack cipher, Bezier curves

Abstract

These days we are constantly sharing and storing sensitive information online. From credit card numbers to personal identity details, our data is vulnerable to cyber-attacks and breaches. With the increase in cybercrime and hacking techniques, it is becoming increasingly important to protect our data through encryption.

This work aims to create a secure binary number of the system of encryption and to make cipher analysis impossible. We will combine Knapsack’s cipher with the equations of Bezier curves using the three-pass protocol.

The robustness of the proposed methods has been proved and the high security level by the experimental results, where the proposed methods have been more efficient and complex. The computational complexity of this method has been implemented in detail.

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Author Biography

  • Adil AL-Rammahi, University of Kufa

    Mathematics and Computer Applications/Fractional Numerical

References

[1] Wade Trappe and Lawrence Washington, "Introduction to Cryptography with Coding Theory", Pearson Education, Inc., 2006.

[2] Christof Paar and Jann Pelzl, "Understanding Cryptography, Springer, Berlin, Heidelberg", 2010. DOI: https://doi.org/10.1007/978-3-642-04101-3

[3] A. Menezes, and P. Orschot, "Handbook of Applied Cryptography" ,CRC Press,1996, pp.283-319.

[4] Dwi Liestyowati, "Public Key Cryptography" Journal of Physics Conference Series 1477:052062, March 2020. DOI: https://doi.org/10.1088/1742-6596/1477/5/052062

[5] Richard A. Mollin, "An Introduction to Cryptography" Journal Discrete Mathematical& Applications, 2000.

[6] R. Merkle, M. Hellman, "Hiding Information and Signatures In Trapdoor Knapsacks", IEEE Trans. on Inform. IT-24, 5,Sept., 1978, pp. 525-530. DOI: https://doi.org/10.1109/TIT.1978.1055927

[7] A. Krishna, "An Improvised ECC Mechanism with Probabilistic Approach", Information Security Journal: A Global Perspective ,vol 21, no.1, 2012, pp. 28-35. DOI: https://doi.org/10.1080/19393555.2011.629338

[8] S. Kallpha, J. Abdul Sada , H. Hussain, "New Public-Key cryptosystem", International Journal of Systems Science,Vol.1, No.1,(2012, Pp. 205-215. DOI: https://doi.org/10.1080/00207729008910354

[9] Y. Lu , J. Li, "New forward-secure public-key encryption without random oracles, International Journal of Computer Mathematics", Vol. 90, Issue 12, , 2013, pp. 2603-2613. DOI: https://doi.org/10.1080/00207160.2013.807915

[10] T. Yamada, K. Watanabe And S. Kataoka, "Algorithms to Solve the Knapsack Constrained Maximum Spanning Tree Problem", International Journal Of Computer Mathematics, Taylor & Francis Group Publisher, Vol. 82, No. 1, January, 2013, pp.23–34. DOI: https://doi.org/10.1080/00207160412331290667

[11] O.K. Peasah, S. K. Amponsah and D. Asamoah, "Knapsack problem: A case study of garden city radio (GCR), Kumasi", Ghana,African Journal of Mathematics and Computer Science Research , Academic Journals Vol. 4(4), April, 2011, pp. 170 -176.

[12] J. Roland, Y. Smet, and J. Fegueira, "The Inverse Multi-Objective {0,1}-Knapsack Problem Under the Chebyshev Distance", Technical Report Number, 2011, pp,1-9.

[13] B. C. Dean, M. X. Goemans, J. Vondrak, "Approximating the Stochastic Knapsack Problem: The Benefit of Adaptivity", Mathematics of Operations Research, Inform Publisher Vol. 33, No. 4, November,. 2008, pp. 945–964. DOI: https://doi.org/10.1287/moor.1080.0330

[14] P. O. Bonsu, and M. A. Boateng, "Improved shield for knapsack sprayers", Agricultural Science Research Journals, International Research Journals publisher, Vol. 3(3), , March, 2013, pp. 93-96.

[15] N. Vinothini, "Asymmetric Key Cryptography using Merkle-Hellman Knapsack Method and Genetic Algorithm", Journal of Computer Engineering and Applications, Vol. XII, Issue I, Jan. 18, 2018, pp.1-9.

[16] Hamza B. Habib, Wadhah A. Hussein, Diana S. Mahdi "Improving the security of the Knapsack Cryptosystem by using Legendre Symbol", Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12(11), , 2021, pp. 2249-2255.

[17] Adil Alrammahi, "Image Cryptography with Least Squares Approximations", JCS, science publications, 15,11, 2019, pp. 1659-1668. DOI: https://doi.org/10.3844/jcssp.2019.1659.1668

[18] Sujit Das, Bibhas Dhara, "A new image encryption method using Bezier curve", Multimedia Tools and Applications, 82,30, 2023, pp. 1-42. DOI: https://doi.org/10.1007/s11042-023-14919-8

[19] Nur Ismail, Yushalify Misro, "An Improved Image Encryption Algorithm Based on Bézier Coefficients Matrix", Journal of King Saud University - Computer and Information Sciences 34(1), 2022, pp. 1-8 DOI: https://doi.org/10.1016/j.jksuci.2022.10.005

[20] Hala Abdul Wahab, Tanya Jaber, "Using Chebyshev Polynomial and Quadratic Bezier Curve for Secure Information Exchange", Eng. Tech, 34, 5, 2016, pp. 666-674.

[21] B. Srividya, S. Akhila, "Selective Encryption of Video Frames Using Bezier Curve Over Galois Field GF (P^m)", ICTCS 16, 2016, pp. 33-44. DOI: https://doi.org/10.1145/2905055.2905341

[22] Armstrong, Jim., " Quadratic Bézier curve", TecNote TN- 05-003, 2005.

[23] Burkardt John. "Forcing Bezier Interpolation." Archived from the original on, 2013, pp. 12-25.

[24] M. Fadhel, "Analysis of Bézier Method Numerically with Applications", M.Sc thesis, Department of mathematics, College of Science, University of Kufa, 2009.

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Published

2026-01-05

How to Cite

AL-Rammahi, A., & Alshaeer, B. . (2026). Crypto Algorithm for Binary Numbers using Knapsack via Bezier curve. Journal of Kufa for Mathematics and Computer, 12(1), 12-16. https://doi.org/10.31642/JoKMC/2018/120103

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