Due to the transparency of the wireless channel, users in multiple-key environment are vulnerable to eavesdropping during the process of uploading personal data and re-encryption keys. Besides, there is additional burden of key management arising from multiple keys of users. In addition, profile matching using inner product between vectors cannot effectively filter out users with ulterior motives. To tackle the above challenges, we first improve a homomorphic re-encryption system (HRES) to support a single homomorphic multiplication and arbitrarily many homomorphic additions. The public key negotiated by the clouds is used to encrypt the users’ data, thereby avoiding the issues of key leakage and key management, and the privacy of users’ data is also protected. Furthermore, our scheme utilizes the homomorphic multiplication property of the improved HRES algorithm to compute the cosine result between the normalized vectors as the standard for measuring the users’ proximity. Thus, we can effectively improve the social experience of users.
An algebraic version of the multiplication property of the Fredholm index
