Authors : Kundan Kumar Gupta; Manisha Priya; Aakash Kumar

Volume/Issue : Volume 11 - 2026, Issue 8 - August

Google Scholar : https://tinyurl.com/37nfhf3c

DOI : https://doi.org/10.38124/ijisrt/26aug1487

Note : A published paper may take 4-5 working days from the publication date to appear in PlumX Metrics, Semantic Scholar, and ResearchGate.

Abstract : Group signature schemes are essential cryptographic primitives that enable authorized members to sign messages on behalf of a group while maintaining anonymity against verifiers. However, many existing schemes face challenges regarding computational efficiency, public key scalability, and robust security against coalition attacks. This study addresses these limitations by proposing three novel group signature constructions. The first scheme is based on the Discrete Logarithm Problem (DLP) and focuses on providing high-speed verification. The second scheme introduces an identitybased (ID-based) structure utilizing both factoring and DLP to simplify key management. The third scheme leverages the algebraic properties of bilinear pairings to create an ID-based group signature that achieves short signature lengths and resists key escrow issues. Formal security analysis demonstrates that the proposed schemes satisfy critical requirements, including unforgetability, anonymity, linkability, traceability, and coalition resistance. Furthermore, a performance comparison indicates that the proposed structures significantly reduce computational complexity in signature generation and verification phases compared to established models like the Lee and Wang-Fu schemes. These findings suggest that the integrated approach of using DLP and bilinear pairings offers a scalable and secure framework suitable for modern digital infrastructure, including e-voting and anonymous electronic tendering systems.

Keywords : Bilinear Pairings, Cryptography, Discrete Logarithm Problem, Group Signature, Signature Scheme.

References :

1. Agarwal, A., & Saraswat, R. (2013). A survey of group signature technique, its applications and attacks. International Journal of Engineering and Innovative Technology, 2(10).
2. Ateniese, G., & Tsudik, G. (1999). Some open issues and new directions in group signature schemes. In Financial Cryptography (FC’99), LNCS 1648, 196–211. Springer.
3. Ateniese, G., Camenisch, J., Joye, M., & Tsudik, G. (2000). A practical and provably secure coalition-resistant group signature scheme. In Advances in Cryptology – CRYPTO 2000, LNCS 1880, 255–270. Springer.
4. Camenisch, J. (1997). Efficient and generalized group signatures. In EUROCRYPT 1997, LNCS 1233, 465–479. Springer.
5. Camenisch, J., & Stadler, M. (1997). Efficient group signature schemes for large groups. In CRYPTO 1997, LNCS 1294, 410–424. Springer.
6. Camenisch, J., Piveteau, J. M., & Stadler, M. (1994). Blind signatures based on the discrete logarithm problem. In EUROCRYPT 1994, 428–432.
7. Cao, Z. (2005). Untraceability of two group signature schemes. Cryptology ePrint Archive, Report 2005/055.
8. Cheng-Chi, L., Chang, T. Y., & Hwang, M. S. (2010). A new group signature scheme based on the discrete logarithm. Journal of Information Assurance and Security, 5, 54–57.
9. Furukawa, J., & Imai, H. (2006). An efficient group signature scheme from bilinear maps. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, E89-A(5).
10. Joye, M., Kim, S., & Lee, N. (1999). Cryptanalysis of two group signature schemes. In Information Security 1999, LNCS 1729, 271–275. Springer.
11. Lee, W. B., & Chang, C. C. (1998). Efficient group signature scheme based on discrete logarithm problem. IEE Proceedings – Computers and Digital Techniques, 145(1), 15–18.
12. Tseng, Y. M., & Jan, J. K. (1998). A novel ID-based group signature. In Workshop on Cryptology and Information Security, 159–164.
13. Wang, X., & Fu, F. (2003). A secure group signature scheme. Journal of Electronics and Information.
14. Xia, S., & You, J. (2002). A group signature scheme with strong separability. The Journal of Systems and Software, 60(3), 177–182.
15. Zhang, J., Wu, Q., & Wang, Y. (2005). A new efficient group signature with forward security. Informatica, 29, 321–325.
16. Zhou, S., & Lin, D. (2005). On anonymity of group signatures. In CIS 2005, LNAI 3802, 131–136. Springer.