Research Article
Open Access
A Conditional Privacy-Preserving Short Signature Scheme for Industrial Internet of Things
1
Department of Mathematics, D.A.V. (P.G.) College, Muzaffarnagar, Affiliated to Maa Shakumbhari University, Uttar Pradesh 251001, India
2
Chaudhary Charan Singh University, Meerut, Uttar Pradesh 250004, India
* Corresponding Author:
Pushpendra Kumar Vashishtha,
[email protected]
Volume 2, Issue 1
2026
Received: 01 January 2026
Accepted: 23 March 2026
Published: 24 March 2026
Article Information
Published in
Journal of Reliable and Secure Computing
Volume/Issue
Volume 2, Issue 1, 2026
Pages
39-49
Cited by
1 (Crossref)
2 (Scopus)
Abstract
Securely transmitting a large amount of data in a short time is a serious challenge in today's digital age. Cryptographic primitives can significantly alleviate this problem. The invention of digital signatures represents a major advance in this area. The Certificateless Aggregate Signature (CLAS) scheme is a cryptographic primitive that greatly reduces the computation cost by aggregating several signatures into a single short signature. However, the costs of aggregate signatures have not been reduced to the desired extent. In this paper, we propose a certificateless aggregate signature scheme that requires only two bilinear pairing operations to verify both a single signature and an aggregate signature, regardless of the number of signers. This makes the scheme highly suitable for low-cost IoT applications. In this scheme, we also present a Type I attack on Horng et al.'s scheme and provide an improved version.
Graphical Abstract
Keywords
certificateless
aggregate signature
low cost
Type I attack
conditional privacy
Data Availability Statement
Data will be made available on request.
Funding
This work was supported without any funding.
Conflicts of Interest
The authors declare no conflicts of interest.
AI Use Statement
The authors declare that no generative AI was used in the preparation of this manuscript.
Ethical Approval and Consent to Participate
Not applicable.
References
- Li, S., Xu, L., & Zhao, S. (2015). The internet of things: A survey. Information Systems Frontiers, 17(2), 243-259.
[CrossRef] [Google Scholar] - Diffie, W., & Hellman, M. (1976). New directions in cryptography. IEEE Transactions on Information Theory, 22(6), 644-654.
[CrossRef] [Google Scholar] - Shamir, A. (1984, August). Identity-based cryptosystems and signature schemes. In Workshop on the theory and application of cryptographic techniques (pp. 47-53). Berlin, Heidelberg: Springer Berlin Heidelberg.
[CrossRef] [Google Scholar] - Zhang, L., & Zhang, F. (2009). A new certificateless aggregate signature scheme. Computer Communications, 32(6), 1079-1085.
[CrossRef] [Google Scholar] - Al-Riyami, S. S., & Paterson, K. G. (2003, November). Certificateless public key cryptography. In International conference on the theory and application of cryptology and information security (pp. 452-473). Berlin, Heidelberg: Springer Berlin Heidelberg.
[CrossRef] [Google Scholar] - Raya, M., & Hubaux, J. P. (2007). Securing vehicular ad hoc networks. Journal of computer security, 15(1), 39-68.
[CrossRef] [Google Scholar] - He, D., Zeadally, S., Xu, B., & Huang, X. (2015). An efficient identity-based conditional privacy-preserving authentication scheme for vehicular ad hoc networks. IEEE Transactions on Information Forensics and Security, 10(12), 2681-2691.
[CrossRef] [Google Scholar] - Zhong, H., Han, S., Cui, J., Zhang, J., & Xu, Y. (2019). Privacy-preserving authentication scheme with full aggregation in VANET. Information Sciences, 476, 211-221.
[CrossRef] [Google Scholar] - Wang, H., Wang, L., Zhang, K., Li, J., & Luo, Y. (2022). A conditional privacy-preserving certificateless aggregate signature scheme in the standard model for VANETs. IEEE Access, 10, 15605-15618.
[CrossRef] [Google Scholar] - Li, J., Yuan, H., & Zhang, Y. (2016). Cryptanalysis and improvement of certificateless aggregate signature with conditional privacy-preserving for vehicular sensor networks. Cryptology ePrint Archive.
[Google Scholar] - Yang, X., Wang, W., Tian, T., & Wang, C. (2023). Cryptanalysis and improvement of a blockchain-based certificateless signature for IIoT devices. IEEE Transactions on Industrial Informatics, 20(2), 1884-1894.
[CrossRef] [Google Scholar] - Shim, K. A. (2024). A secure certificateless signature scheme for cloud-assisted Industrial IoT. IEEE Transactions on Industrial Informatics, 20(4), 6834-6843.
[CrossRef] [Google Scholar] - Boneh, D., Gentry, C., Lynn, B., & Shacham, H. (2003, May). Aggregate and verifiably encrypted signatures from bilinear maps. In International conference on the theory and applications of cryptographic techniques (pp. 416-432). Berlin, Heidelberg: Springer Berlin Heidelberg.
[CrossRef] [Google Scholar] - Peter, O., Pradhan, A., & Mbohwa, C. (2023). Industrial internet of things (IIoT): Opportunities, challenges, and requirements in manufacturing businesses in emerging economies. Procedia Computer Science, 217, 856-865.
[CrossRef] [Google Scholar] - Hou, K., Diao, X., Shi, H., Ding, H., Zhou, H., & De Vaulx, C. (2023). Trends and challenges in AIoT/IIoT/IoT implementation. Sensors, 23(11), 5074.
[CrossRef] [Google Scholar] - Olanrele, O., Ajagbe, S., Ilori, A., & Adeyemi, O. (2025). The industrial internet of things (IIoT): Overview, architecture, challenges, and possible solutions. Computational Intelligence in Industry 4.0 and 5.0 Applications, 37-60.
[Google Scholar] - Gentry, C., & Ramzan, Z. (2006). Identity-based aggregate signatures. International Workshop on Public Key Cryptography, 257-273.
[CrossRef] [Google Scholar] - Gong, Z., Long, Y., Hong, X., & Chen, K. (2007, July). Two certificateless aggregate signatures from bilinear maps. In Eighth ACIS international conference on software engineering, artificial intelligence, networking, and parallel/distributed computing (SNPD 2007) (Vol. 3, pp. 188-193). IEEE.
[CrossRef] [Google Scholar] - Huang, X., Mu, Y., Susilo, W., Wong, D. S., & Wu, W. (2007, July). Certificateless signature revisited. In Australasian conference on information security and privacy (pp. 308-322). Berlin, Heidelberg: Springer Berlin Heidelberg.
[CrossRef] [Google Scholar] - Xiong, H., Guan, Z., Chen, Z., & Li, F. (2013). An efficient certificateless aggregate signature with constant pairing computations. Information Sciences, 219, 225-235.
[CrossRef] [Google Scholar] - Horng, S., Tzeng, S., Huang, P., Wang, X., Li, T., & Khan, M. (2015). An efficient certificateless aggregate signature with conditional privacy-preserving for vehicular sensor networks. Information Sciences, 317, 48-66.
[CrossRef] [Google Scholar] - Thumbur, G., Rao, G., Reddy, P., Gayathri, N., Reddy, D., & Padmavathamma, M. (2020). Efficient and secure certificateless aggregate signature-based authentication scheme for vehicular ad hoc networks. IEEE Internet of Things Journal, 8(3), 1908-1920.
[CrossRef] [Google Scholar] - Kar, J., Liu, X., & Li, F. (2021). CL-ASS: An efficient and low-cost certificateless aggregate signature scheme for wireless sensor networks. Journal of Information Security and Applications, 61, 102905.
[CrossRef] [Google Scholar] - Vashishtha, P., & Kumari, S. (2025). Cryptanalysis and improvement on low-cost CL-ASS for wireless sensor networks. International Conference on Network Security and Blockchain Technology, 19-29.
[CrossRef] [Google Scholar] - Xiong, W., Wang, R., Wang, Y., Wei, Y., Zhou, F., & Luo, X. (2022). Improved certificateless aggregate signature scheme against collusion attacks for VANETs. IEEE Systems Journal, 17(1), 1098-1109.
[CrossRef] [Google Scholar] - Vashishtha, P., & Kumari, S. (2025). An improved collusion resistant certificateless aggregate signature scheme for VANETs. International Conference on Mathematics and Computing, 13-24.
[CrossRef] [Google Scholar] - Pointcheval, D., & Stern, J. (1996). Security proofs for signature schemes. International Conference on the Theory and Applications of Cryptographic Techniques, 387-398.
[CrossRef] [Google Scholar] - Mei, Q., Xiong, H., Chen, J., Yang, M., Kumari, S., & Khan, M. (2020). Efficient certificateless aggregate signature with conditional privacy preservation in IoV. IEEE Systems Journal, 15(1), 245-256.
[CrossRef] [Google Scholar] - Liang, Y., & Liu, Y. (2022). Analysis and improvement of an efficient certificateless aggregate signature with conditional privacy preservation in VANETs. IEEE Systems Journal, 17(1), 664-672.
[CrossRef] [Google Scholar] - Deng, L., Wen, J., Gao, Y., Wang, N., Huang, H., & Li, S. (2024). Certificateless aggregate signature scheme with security proofs in the standard model suitable for Internet of Vehicles. IEEE Internet of Things Journal, 11(17), 28765-28773.
[CrossRef] [Google Scholar] - Chen, C., Li, Z., Das, A., Chaudhry, S., & Lorenz, P. (2024). Provably secure authentication scheme for fog computing-enabled intelligent social internet of vehicles. IEEE Transactions on Vehicular Technology, 73(9), 13600-13610.
[CrossRef] [Google Scholar]
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APA Style
Vashishtha, P. K., & Kumari, S. (2026). A Conditional Privacy-Preserving Short Signature Scheme for Industrial Internet of Things. Journal of Reliable and Secure Computing, 2(1), 39–49. https://doi.org/10.62762/JRSC.2026.376190
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TY - JOUR AU - Vashishtha, Pushpendra Kumar AU - Kumari, Saru PY - 2026 DA - 2026/03/24 TI - A Conditional Privacy-Preserving Short Signature Scheme for Industrial Internet of Things JO - Journal of Reliable and Secure Computing T2 - Journal of Reliable and Secure Computing JF - Journal of Reliable and Secure Computing VL - 2 IS - 1 SP - 39 EP - 49 DO - 10.62762/JRSC.2026.376190 UR - https://www.icck.org/article/abs/JRSC.2026.376190 KW - certificateless KW - aggregate signature KW - low cost KW - Type I attack KW - conditional privacy AB - Securely transmitting a large amount of data in a short time is a serious challenge in today's digital age. Cryptographic primitives can significantly alleviate this problem. The invention of digital signatures represents a major advance in this area. The Certificateless Aggregate Signature (CLAS) scheme is a cryptographic primitive that greatly reduces the computation cost by aggregating several signatures into a single short signature. However, the costs of aggregate signatures have not been reduced to the desired extent. In this paper, we propose a certificateless aggregate signature scheme that requires only two bilinear pairing operations to verify both a single signature and an aggregate signature, regardless of the number of signers. This makes the scheme highly suitable for low-cost IoT applications. In this scheme, we also present a Type I attack on Horng et al.'s scheme and provide an improved version. SN - 3070-6424 PB - Institute of Central Computation and Knowledge LA - English ER -
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@article{Vashishtha2026A,
author = {Pushpendra Kumar Vashishtha and Saru Kumari},
title = {A Conditional Privacy-Preserving Short Signature Scheme for Industrial Internet of Things},
journal = {Journal of Reliable and Secure Computing},
year = {2026},
volume = {2},
number = {1},
pages = {39-49},
doi = {10.62762/JRSC.2026.376190},
url = {https://www.icck.org/article/abs/JRSC.2026.376190},
abstract = {Securely transmitting a large amount of data in a short time is a serious challenge in today's digital age. Cryptographic primitives can significantly alleviate this problem. The invention of digital signatures represents a major advance in this area. The Certificateless Aggregate Signature (CLAS) scheme is a cryptographic primitive that greatly reduces the computation cost by aggregating several signatures into a single short signature. However, the costs of aggregate signatures have not been reduced to the desired extent. In this paper, we propose a certificateless aggregate signature scheme that requires only two bilinear pairing operations to verify both a single signature and an aggregate signature, regardless of the number of signers. This makes the scheme highly suitable for low-cost IoT applications. In this scheme, we also present a Type I attack on Horng et al.'s scheme and provide an improved version.},
keywords = {certificateless, aggregate signature, low cost, Type I attack, conditional privacy},
issn = {3070-6424},
publisher = {Institute of Central Computation and Knowledge}
}
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