Bilinear Pairings: A Secured Outsourcing with a Single Server

Qing Ying *

College of Science, North China University of Technology, Beijing-100144, P. R. China.

*Author to whom correspondence should be addressed.


The computation of bilinear pairs is the most computationally expensive computation for bilinear pair-based cryptographic protocols in practice. Currently, most bilinear pairing outsourcing algorithms have little checkability, or the outsourcer requires two servers for expensive calculations. In this paper, we propose an efficient and secure single-server bilinear pairing outsourcing algorithm, which allows the outsourcing party to detect dishonest errors in cloud servers with probability 1, and the outsourcing party does not need to perform some complex computations.

Keywords: Elliptic curve, outsourcing, bilinear pairing

How to Cite

Ying, Q. (2024). Bilinear Pairings: A Secured Outsourcing with a Single Server. Asian Journal of Mathematics and Computer Research, 31(2), 87–95.


Download data is not yet available.


Chen X F, Li J, Ma J F, et al. New algorithms for secure outsourcing of modular exponentiations. IEEE Trans Parall Distrib Syst. 2014;25:2386–2396.

Chaum D, Pedersen T. Wallet databases with observers. Proceedings of 12th Annual Conference on Advances in Cryptology. Berlin: Springer. 1992;89–105.

Hohenberger S, Lysyanskaya A. How to securely outsource cryptographic computations. Proceedings of the 2nd International Conference on Theory of Cryptography. Berlin: Springer. 2005;264–282.

Green M, Hohenberger S, Waters B. Outsourcing the decryption of ABE ciphertexts. Proceedings of the 20th USENIX Conference on Security. New York: ACM. 2011;34.

Qianqian Su;Rui Zhang;Rui Xue. Secure Outsourcing Algorithms for Composite Modular Exponentiation Based on Single Untrusted Cloud. The Computer Journal. 2020;63(8):1271-1271.

Yunhai Zheng and Chengliang Tian. Lattice-Based Cryptanalysis on Outsourcing Scheme of Modular Exponentiations ExpSOS.Journal of Frontiers of Computer Science and Technology. 2022;16(05):1087-1095.

Lai JZ, Deng RH, Guan CW, et al. Attribute-based encryption with verifiable outsourced decryption. IEEE Trans Inf Foren Secur. 2013;8:1343–1354.

Chevallier-Mames B, Coron J, McCullagh N, et al. Secure delegation of elliptic-curve pairing. Proceedings of the 9th IFIP WG 8.8/11.2 International Conference on Smart Card Research and Advanced Application. Berlin: Springer. 2010;24–35.

Tsang P, Chow S, Smith S. Batch pairing delegation. Proceedings of the 2nd International Workshop on Security. Berlin: Springer. 2007;74–90.

Chow S, Au M, Susilo W. Server-aided signatures verification secure against collusion attack. Proceedings of the 6th ACM Symposium on Information, Computer and Communications Security. New York: ACM, 2011. 401–405.

Chen XF, Susilo W, Li J, et al. Efficient algorithms for secure outsourcing of bilinear pairings. Theor Comput Sci. 2015;562:112–121.

Tian HB, Zhang FG, Ren K. Secure bilinear pairing outsourcing made more efficient and flexible. Proceedings of the 10th ACM Symposium on Information, Computer and Communications Security. New York: ACM. 2015;417–426.

Min dong, Yanli Ren, Xinpeng Zhang. Fully Verifiable Algorithm for Secure Outsourcing of Blinear Pairing in Cloud Computing. KSII Transactions on Internet and Information Systems. 2017;7(11):3648-3663.

Hohenberger S, Lysyanskaya A. How to Securely Outsource Cryptographic Proc. TCC, LNCS Springer-Verlag: New York, NY, USA. 2005;3378:264-282.

Ren Y, Ding N, Wang T. et al., New algorithms for verifiable outsourcing of bilinear pairing, Science China Information Sciences. 2016;59:099103.