In the field of the Telecare Medicine Information System, recent researches have focused on consummating more convenient and secure healthcare delivery services for patients. In order to protect the sensitive information, various attempts such as access control have been proposed to safeguard patients' privacy in this system. However, these schemes suffered from some certain security defects and had costly consumption, which were not suitable for the telecare medicine information system. In this paper, based on the elliptic curve cryptography, we propose a secure and efficient two-factor mutual authentication and key agreement scheme to reduce the computational cost. Such a scheme enables to provide the patient anonymity by employing the dynamic identity. Compared with other related protocols, the security analysis and performance evaluation show that our scheme overcomes some well-known attacks and has a better performance in the telecare medicine information system.

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Attribute-based encryption (ABE) is a promising cryptographic tool for data owner (DO) to realize fine-grained date sharing in the cloud computing. In the encryption of most existing ABE schemes, a substantial number of modular exponentiations are often required; the computational cost of it is growing linearly with the complexity of the access policy. Besides, in the most existing ABE with outsourced decryption, the computation cost of generating transformation key is growing linearly with the number of attributes associated with user private key; these computations are prohibitively high for mobile device users, which becomes a bottleneck limiting its application. To address the above issues, we propose a secure outsourcing algorithm for modular exponentiation in one single untrusted server model and a new method to generate the transformation key. Based on these techniques and Brent Waters's ciphertext-policy ABE scheme, we propose an ABE scheme with verifiable outsourced both encryption and decryption, which can securely outsource encryption and decryption to untrusted encryption service provider (ESP) and decryption service provider (DSP), respectively, leaving only a constant number of simple operations for the DO and eligible users to perform locally. In addition, both DO and the eligible users can check the correctness of results returned from the ESP and the DSP with a probability, respectively. Finally, we provide the experimental evaluation and security analysis of our scheme, which indicates that our construction is suitable for the mobile environment.

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