Secure Obfuscation of Conditional Re-encryption with Keyword Search

Several results of secure obfuscation for particular function families have been raised out in despite of the general impossibility result presented by Barak et al. A special re-encryption function was securely obfuscated by Hohenberger et al. in TCC´07. The re-encryption function constructed by them has particular property that the second level cipher texts are in different form with the first level cipher texts, so the second level cipher texts cannot be re-encrypted for multi-use. Besides, decryption of the second level cipher texts need to be fulfilled by brute force search on the message space. In this paper we propose a new re-encryption function which can be securely obfuscated and supports multi-use transfer. Moreover, the decryption of the second level cipher texts does not need brute force search. Besides, we extend this re-encryption function to a conditional re-encryption with keyword search scheme, which only transfers those first level cipher texts satisfying some keyword condition to the second level cipher texts. Also we give out the obfuscation of the function family and the security analysis.