Journal of Networks, Vol 6, No 4 (2011), 631-637, Apr 2011

An Identity Based Aggregate Signature from Pairings

Yike Yu, Xuefeng Zheng, Hua Sun


An aggregate signature is a useful digital signature that supports aggregation: Given n signatures on n distinct messages from n distinct users, aggregate signature scheme is possible to aggregate all these signature into a single short signature. This single signature, along with the n original messages will convince any verifier that the n users did indeed sign the n original messages respectively (i.e., for i=1,...,n user i signed message  mi). In this paper, we propose an identity based aggregate signature scheme which requires constant pairing operations in the verification and the size of aggregate signature is independent of the number of signers. We prove that the proposed signature scheme is secure against existential forgery under adaptively chosen message and identity attack in the random oracle model assuming the intractability of the computational Diffie-Hellman problem.


Aggregate signature;Bilinear pairings;Identity-based cryptograph;Computational Diffie-Hellman problem


[1] A. Shamir, “Identity-based cryptosystems and signature schemes,” Proceedings of Crypto’84, LNCS Vol.196, pp.47-53, Springer-Verlag, 1985.

[2] D. Boneh and M. Franklin, “Identity Based Encryption from the Weil Paring,” Proceedings of Crypto’ 01, LNCS, Vol.2139, pp.213-229, Springer-Verlag, 2001.

[3] K. Paterson, “ID-based Signatures from Pairings on Elliptic Curves,” Available from, 2002.

[4] F. Hess, “Efficient identity based signature schemes based on pairings,” Proceedings of Selected Areas in Cryptography’02, LNCS Vol.2595, pp.310-324, Springer-Verlag, 2003.

[5] J. C. Cha and J. H. Cheon, “An identity-based signature from gap Diffie-Hellman groups,” Proceedings of PKC’03, LNCS Vol.2567, pp.18-30, Springer-Verlag, 2003.

[6] K. G. Paterson and J. C. N. Schuldt, “Efficient identity-based signatures secure in the standard model,” Proceedings of the 11th Australasian Conference on Information Security and Privacy, LNCS Vol.4058. pp. 207-222, Springer-Verlag, 2006.

[7] S. Kent, C. Lynn, and K. Seo, “Secure border gateway protocol (Secure-BGP),” IEEE J. Selected Areas in Comm., 18(4):582–92, April 2000.

[8] D. Boneh, C. Gentry, B. Lynn and H. Shacham, “Aggregate and verifiably encrypted signatures from bilinear maps,” Advances in Cryptology - Eurocrypt 2003, LNCS Vol.2656, pp.416-432, Springer-Verlag, 2003.

[9] Z. H. Shao, “Enhanced Aggregate Signatures from Pairings, ” SKLOIS Conference on Iformation Security and Cryptology CISC 2005, LNCS Vol.3822. pp.140-149, Berlin: Springer-Veralg, 2003.

[10] A. Lysyanskaya, S. Micali, L. Reyzin, et al., “Sequential Aggregate Signatures from Trapdoor Homomorphic Permutations,” Proceedings of EUROCRYPT 2004: LNCS Vol.3027. pp.74-90, Berlin: Springer -Verlag, 2004.

[11] A. Mihara, K. Tanaka, “Universal designated-verifier signature with aggregation,” In Proceedings-3rd International Conference on Information Technology and Applications, ICITA 2005, IEEE Press, 2005(II):514-519.

[12] S. Lu, R. Ostrovsky, A. Sahai, et al., “Sequential Aggregate Signatures and Multi signatures without Random Oracles,” Advances in Cryptology-EUROCRYPT 2006: LNCS Vol.4004. pp.465-485, Berlin: Springer-Verlag, 2006.

[13] Y. Mu, W. Susilo and H. F. Zhu, “Compact Sequential Aggregate Signatures,” In Proceedings of the 2007 ACM symposium on Applied computing. ACM, pp.249-253, 2007.

[14] M. Bellare, C. Namprempre, G. Neven, “Unrestricted Aggregate Signatures,” In Proceeding of ICALP 2007, LNCS Vol.4596, pp.411-422, Berlin: Springer-Verlag, 2007.

[15] Z. Gong, Y. Long, X. Hong, et al., “Two Certificateless Aggregate Signatures From Bilinear Maps,” Eighth ACIS International Conference on Software Engineering, Artificial Intelligence, Networking, and Parallel/ Distributed Computing, ACIS 2007, IEEE Press 2007:188-193.

[16] J. Li, K. Kim and F. G. Zhang, et al., “Aggregate Proxy Signature and Verifiably Encrypted Proxy Signature,” International Conference on Provable Security 2007. LNCS Vol.4784, pp.208-217, Berlin: Springer-Veralg, 2007.

[17] C. H. Wang, Y. S. Kuo, “An efficient contract signing protocol using the aggregate signature scheme to protect signers’ privacy and promote reliability,” ACM SIGOPS Operating Systems Review (ACM) 2005(39):66-79.

[18] D. F. Yao, R. Tamassia, “Cascaded authorization with anonymous-signer aggregate signatures,” In Proceedings of the 2006 IEEE Workshop on Information Assurance, 2006, pp.84-91, IEEE Press, 2006.

[19] S. B. Wang, Z. F. Cao, Q. Wang, et al., “Authenticated key agreement protocol using bilinear aggregate signatures,” Proceedings of 2005 Global Mobile CongressDelson Group Inc. 2005:328-332.

[20] H. F. Zhu, F. Bao, T. Y. Li, et al., “Sequential Aggregate Signatures for Wireless Routing Protocols,” The 2005 IEEE Wireless Communications and Networking Conference, WCNC 2005, IEEE Press 2005:2436-2439.

[21] B. Wang, J. H. Zhang, Y. F. Guo, “APVP: An Aggregate-Based Path Verification Routing Protocol for the Ad Hoc Networks,” Proceedings of the 2008 International Conference on Computational Intelligence and Security, IEEE Computer Society, Vol. 02, pp. 386-390, 2008.

[22] J. H. Cheon, Y. Kim, and H. J. Yoon, “A New ID-Based Signature with Batch Verification,” Available from

[23] J. Xu,Z. Zhang, D. Feng, “ID-based aggregate signature from bilinear pairings,” Proceedings of the 4th International Conference on Cryptology and Network Security. Berlin: Springer-Verlag, 2005: 110-119.

[24] J. Herranz, “Deterministic identity-based signatures for partial aggregation,” Computer Journal, 49(3): 322-330,2006.

[25] C. Gentry, Z. Ramzan, “Identity-based aggregate signatures,” Proceedings of PKC’06. LNCS Vol.3958, pp 257–273, Springer, 2006.

[26] Z. Wang, H. Chen, D. Ye, et al, “Practical identity-based aggregate signature scheme from bilinear maps,” volume 13(6), pages 684–687. Shanghai Jiao Tong University Press, 2008.

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