The homomorphic proxy re-encryption scheme combines the characteristics of a homomorphic encryption scheme and proxy re-encryption scheme. The proxy can not only convert a ciphertext of the delegator into a ciphertext of the delegatee, but also can homomorphically calculate the original ciphertext and re-encryption ciphertext belonging to the same user, so it is especially suitable for cloud computing. Yin et al. put forward the concept of a strong collusion attack on a proxy re-encryption scheme, and carried out a strong collusion attack on the scheme through an example. The existing homomorphic proxy re-encryption schemes use key switching algorithms to generate re-encryption keys, so it can not resist strong collusion attack. In this paper, we construct the first lattice-based homomorphic proxy re-encryption scheme with strong anti-collusion (HPRE-SAC). Firstly, algorithm TrapGen is used to generate an encryption key and trapdoor, then trapdoor sampling is used to generate a decryption key and re-encryption key, respectively. Finally, in order to ensure the homomorphism of ciphertext, a key switching algorithm is only used to generate the evaluation key. Compared with the existing homomorphic proxy re-encryption schemes, our HPRE-SAC scheme not only can resist strong collusion attacks, but also has smaller parameters.
Keywords: LWE; cloud computing; homomorphic proxy re-encryption; key switching; strong anti-collusion; trapdoor sampling.