In this paper, we propose an efficient authenticated encryption scheme based on elliptic curve cryptography. The proposed scheme does not need to construct any digital signature, so the computation costs can be greatly reduced. In addition, we also use the proposed authenticated encryption scheme to design a secure electronic payment system. The proposed electronic payment system provides the security requirements of confidentiality, authenticity, integrity, privacy protection, and double-spending prevention. According to the results of this paper, the proposed authenticated encryption scheme can be easily implemented in mobile payment environments. Besides, it can be also applied to electronic auction, online meeting, and electronic voting.
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