Abstract The threshold proxy signcryption can implement signature and encryption simultaneously in one logical step, and can be used to realize the decentralized protection of the group signature key, so it is an efficient technology for network security. Currently, most of the existing threshold proxy signcryption schemes are designed based on the traditional public key cryptosystems, and their security mainly depends on the difficulty of the large integer decomposition and the discrete logarithm. However, the traditional public key cryptosystems cannot resist the quantum computer attack, which makes the existing threshold proxy signcryption schemes based on traditional public key cryptosystems insecure against quantum attacks. Motivated by these concerns, we proposed a threshold proxy signcryption scheme based on Multivariate Public Key Cryptosystem (MPKC) which is one of the quantum attack-resistent public key algorithms. Under the premise of satisfying the threshold signcryption requirements of the threshold proxy, our scheme can not only realize the flexible participation of the proxy signcrypters but also resist the quantum computing attack. Finally, based on the assumption of Multivariate Quadratic (MQ) problem and Isomorphism Polynomial (IP) problem, the proof of the confidentiality and the unforgeability of the proposed scheme under the random oracle model is given.

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[21] Zhou M. and Yu Z., “New Double-threshold Proxy Signcryption Scheme from Bilinear Pairings,” Computer Engineering and Applications, vol. 47, no. 32, pp. 98-100, 2011. Li Huixian is an Associate Professor with School of Computer Science and Engineering, Northwestern Polytechnical University, Xi’an, China Her main research interests include information security, cryptography and secure protocols. Gao Jin is currently pursuing the Master degree in School of Computer Science and Engineering, Northwestern Polytechnical University, Xi’an, China. His research interest focuses on attribute- based encryption. Wang Lingyun is currently pursuing the Master degree in School of Computer Science and Engineering, Northwestern Polytechnical University, Xi’an, China His research interest focuses on multivariate public key cryptosystem Pang Liaojun is a full professor with State Key Laboratory of Integrated Services Networks of Xidian University, and at the same time he was a visiting scholar at the Department of Computer Science of Wayne State University of USA His research interests include Internet security, cryptography, secure mobile agent system and e-commerce security technology. He became a Member (M) of IEEE in 2009.