In the research of cryptography, a very important technique is “pairing-based cryptography ”. Its method is based on an element in the additive group G1 and an element in the additive group G2 to perform mapping to generate an element in the multiplicative group G. Pairing is widely used in the field of cryptography and pairing operations are resource-consuming. So, the method of outsourcing pairing calculation has attracted much attention, and Ren et al. proposed a scheme in 2016. It proposes a secure verifiable outsourcing algorithm of single bilinear pairing based on two untrusted servers, and improved verifiability of outsourcing. But the disadvantage of this scheme is existing attack method for verifiability. The attack method proposed by Osmanbey Uzunkol et al. in 2017. So, this paper proposes an improved solution to prevent attacks.
In this paper, we first introduce the algorithm for verifiable outsourcing of bilinear pairings proposed by Ren et al., then presents attack methods of this algorithm proposed by Osmanbey Uzunkol et al. Final, we present our method to improve the algorithm and show it is security for protecting user’s information.
Bilinear pairings, Verifiable outsourcing, Pairing-based cryptography.
Authors and contacts:
Jen-Chien Hsu, Department of Computer Science, National Chengchi University, 64, Sec. 2, Zhi-nan Rd., Taipei 11605, China, firstname.lastname@example.org
Jhe-Wei Lin, Department of Computer Science, National Chengchi University, 64, Sec. 2, Zhi-nan Rd., Taipei 11605, China
Sk Md Mizanur Rahman, Information and Communication Engineering Technology (ICET), School of Engineering Technology and Applied Science (SETAS), Centennial College, Toronto, ON M1G 3T8, Canada
Raylin Tso*, Department of Computer Science, National Chengchi University, 64, Sec. 2, Zhi-nan Rd., Taipei 11605, China, email@example.com
Jen-Chien Hsu, Jhe-Wei Lin, Sk Md Mizanur Rahman, and Raylin Tso, “Security analysis and improvement of verifiable outsourcing of bilinear pairing scheme”, Journal of Computer Security and Data Forensics, Vol. 1, No. 2, pp. 14~27, June 2021.