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Open Access ·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.

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Open Access Research Article

A novel blind signature scheme based on RSA cryptosystem using Tribonacci matrix

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pp. 1735–1752Vol. 29Issue 4April 2026DOI: 10.47974/JDMSC-2556 Crossmark XML
Received:
01 Jan 2025
Published Online:
08 Apr 2026
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2556
Pages:
1735–1752

Abstract

In recent years, there have been innovations in the realm of digital signatures, with extensions and variations that integrate digital signatures with specific protocols to provide additional functionalities not offered by standard signature schemes. While that integrate digital signatures with specific protocols to provide additional functionalities not offered by standard signature schemes. While conventional signatures schemes involve a signer signing message that can be verified by any one, there are situations where the confidentiality of the message is paramount. To address this need, Chaums proposed the concept of blind signatures, this mechanism enables a user to secure a signature on a message while maintaining complete privacy of the message with respect to the signer. The blind signature system protects user privacy which enables its use in e-voting and e-cash systems for anonymous operations. Scientists developed multiple signature schemes which use integer message representation to protect security through integer factorization and modular logarithm problem solutions. The security of these systems needs to be improved according to current assessments. The research presents a new Blind Signature Scheme which combines the RSA cryptosystem with Tribonacci Matrix technology. Our proposed system shows that messages exist as matrices which gain protection through the RSA security model. The study provides a full evaluation of the proposed system’s security measures together with its operational performance.

Keywords

Subject Classifications

11T7115A6011B3914G50

References

[1] W. Diffie and M. Hellman, “New directions in cryptography,” IEEE Trans. Inf. Theory, vol. IT-22, pp. 472–292 (1976), doi: 10.1109/TIT.1976.1055638.
[2] T. Elgamal, “A public key cryptosystem and a signature scheme based on discrete logarithms,” IEEE Trans. Inf. Theory, vol. 31, no. 4, pp. 469–472 (1985), doi: 10.1109/TIT.1985.1057074.
[3] L. Harn and Y. Xu, “Design of generalised ElGamal type digital signature schemes based on discrete logarithm,” Electron. Lett., vol. 30, no. 24, pp. 2025–2026 (1994), doi: 10.1049/el:19941398.
[4] V. R. L. Shen, Y. F. Chung, T. S. Chen, and Y. A. Lin, “A blind signature based on discrete logarithm problem,” Int. J. Innov. Comput. Inf. Control, vol. 7, no. 9, pp. 5403–5416 (2011). [Online]. Available: http://www.ijicic.org/ijicic-10-05047.pdf
[5] R. L. Rivest, A. Shamir, and L. Adleman, “A method for obtaining digital signatures and public-key cryptosystems,” Commun. ACM, vol. 21, no. 2, pp. 120–126 (1978), doi: 10.1145/359340.359342.
[6] Z. Shao, “Signature schemes based on factoring and discrete logarithms,” IEE Proc. Comput. Digit. Tech., vol. 145, no. 1, pp. 33 (1998), doi: 10.1049/ip-cdt:19981773.
[7] S. Inam and R. Ali, “A new ElGamal-like cryptosystem based on matrices over group ring,” Neural Comput. Appl., vol. 29, no. 11, pp. 1279–1283 (2018), doi: 10.1007/s00521-016-2745-2.
[8] S. C. Gupta and M. Sanghi, “A new digital signature scheme using tribonacci matrices,” Int. J. Comput. Inf. Technol., vol. 9, no. 3 (2020), doi: 10.24203/ijcit.v9i3.11.
[9] A. P. Stakhov, “The golden matrices and a new kind of cryptography,” Chaos, Solitons Fractals, vol. 32, pp. 1138–1146 (2007), doi: 10.1016/j.chaos.2006.03.069.
[10] R. Nayak and J. Pradhan, “NTRU digital signature scheme: A matrix approach,” Int. J. Adv. Res. Comput. Sci., vol. 2, no. 1 (2011). [Online]. Available: https://ijarcs.info/index.php/Ijarcs/article/view/255
[11] F. Bani-Ahmad, M. T. A. Shatnawi, Nisaa Tahat, and S. A. Shatnawi, “A new kind of digital signature scheme using golden matrices based on factoring problem,” Int. J. Pure Appl. Math., vol. 107, no. 1 (2016), doi: 10.12732/ijpam.v107i1.5.
[12] U. R. Bodasingi and S. Gunupuru, “New digital signature scheme based on RSA using circulant matrix,” SN Comput. Sci., vol. 4, pp. 275 (2023), doi: 10.1007/s42979-023-01694-4.
[13] M. E. O. Ebadati, F. Eshghi, and A. Zamani, “A hybrid encryption algorithm for security enhancement of wireless sensor networks: A supervisory approach to pipelines,” Comput. Model. Eng. Sci., vol. 122, no. 1, pp. 323–349 (2020), doi: 10.32604/cmes.2020.08079.
[14] A. Ghasemzadeh and O. R. B. Speily, “A novel method for image encryption using modified logistic map,” J. Inf. Syst. Telecommun., vol. 6, no. 4, pp. 220–227 (2018), doi: 10.7508/jist.2018.04.005.
[15] M. Basu and M. Das, “Tribonacci matrices and a new coding theory,” Discrete Math., Algorithms Appl., vol. 6, no. 1 (2014), doi: 10.1142/S1793830914500086.
[16] D. Chaum, “Blind signatures for untraceable payments,” in Advances in Cryptology. Springer (1983). [Online]. Available: https://sceweb.sce.uhcl.edu/yang/teaching/csci5234WebSecurityFall2011/Chaum-blind-signatures.PDF
[17] N. Singh and S. Das, “A novel proficient blind signature scheme using ECC,” IJCA Proc. Int. Conf. ETCC-2014 (2014). [Online]. Available: https://www.ijcaonline.org/proceedings/etcc/number1/17905-1417/
[18] N. Singh and S. Das, “Cryptanalysis of blind signature schemes,” Int. J. Comput. Appl., vol. 71, no. 19 (2013). [Online]. Available: http://paper.ijcsns.org/07_book/201405/20140513.pdf
[19] A. P. Stakhov, V. Massingue, and A. Sluchenkova, Introduction into Fibonacci Coding and Cryptography. Kharkov: Osnova (1999). ISBN: 5-7768-0638-0.
[20] S. Das and P. Chattopadhyay, “Matrix-based cryptographic transformations using Fibonacci and related sequences,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 24, no. 2, pp. 445–460 (2021).
[21] B. Patel and H. Shah, “Tribonacci and higher-order recurrence relations in secure message encoding,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 26, no. 3, pp. 611–627 (2023).
[22] P. Sen and R. Kumar, “Secure message representation using matrix exponentiation approaches,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 26, no. 1, pp. 301–318 (2023).
[23] R. Thakur and M. Gupta, “Efficient key generation techniques for lightweight public-key cryptography,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 23, no. 1, pp. 129–143 (2020).
[24] M. N. Alam, “Performance analysis of low-complexity blind signature protocols with modular arithmetic,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 22, no. 3, pp. 545–559 (2019).

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