Proxy Re-Encryption Based on Homomorphic Encryption

In this paper, we propose an homomorphic proxy re-encryption scheme (HPRE) that allows different users to share data they outsourced homomorphically encrypted using their respective public keys with the possibility by next to process such data remotely. Its originality stands on a solution we propose so as to compute the difference of data encrypted with Damgard-Jurik cryptosystem. It takes also advantage of a secure combined linear congruential generator that we implemented in the Damgard-Jurik encrypted domain. Basically, in our HPRE scheme, the two users, the delegator and the delegate, ask the cloud server to generate an encrypted noise based on a secret key, both users previously agreed on. Based on our solution to compute the difference in Damgard-Jurik encrypted domain, the cloud computes in clear the differences in-between the encrypted noise and the encrypted data of the delegator, obtaining thus blinded data. In order the delegate gets access to the data, the cloud just has to encrypt these differences using the delegate's public key and then removes the noise. This solution doesn't need extra communication between the cloud and the delegator. Our HPRE was implemented in the case of the sharing of uncompressed images stored in the cloud showing good time computation performance, it is unidirectional and collusion-resistant. Nevertheless, it is not limited to images and can be used with any kinds of data.