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With the development of modern Internet and mobile networks, there is an increasing need for collaborative privacy-preserving applications. Secure multi-party computation (SMPC) gives a general solution to these applications and has become a hot topic. Yao's garbled circuit approach is a leading method in designing protocols for secure two-party computation (2PC), which is a very important base in SMPC. However, there are only few protocols obtaining the fairness of secure 2PC, and only one of them was constructed within the standard simulation framework but with very low efficiency. In this paper, we propose an efficient fair secure Yao's garbled circuit protocol within the universally composable (UC) framework. By comparing with all other fair secure Yao's protocols, our new protocol enjoys three advantages. First, our protocol is more efficient than any other fair secure Yao's protocols within the standard simulation framework. Second, our protocol is the first fair UC-secure Yao's garbled circuit protocol, so it is more secure than other fair Yao's protocols. Third, there does not require any third party involved in our protocol; thus, it is very suitable for many applications.

Qiu et al. made a security analysis about the protocols of Chaudhry et al. and Kumari et al. in 2018, and they pointed out that there are many security weaknesses in the protocols. To improve the security, Qiu et al. proposed an advanced authentication scheme for Session Initiation Protocol on the basis of the previous protocols and claimed that their own protocol was very secure and practical. However, we demonstrate that the protocol of Qiu et al. has a serious mistake which causes their protocol cannot be executed normally. Beyond that, we also find out that their protocol cannot withstand insider attack and denial service attack. In order to remove these weaknesses, we propose an efficient provably secure mutual authentication scheme. Furthermore, our scheme provides security analysis with the help of Burrows-Abadi-Needham (BAN) logic. Compared with their protocol, ours has greater security and better performance.

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