Lattice-based Fuzzy Conditional Proxy Re-encryption

As an extension to conditional proxy re-encryption, fuzzy conditional proxy re-encryption allows for a proxy to re-encrypt a ciphertext only if it satisfies some t-out-of-d threshold condition. Therefore, it is more desirable in some applications where fine-grained control of the decryption delegation is required. In this paper, we construct the first lattice-based fuzzy conditional proxy re-encryption scheme as a post-quantum alternative to this primitive. In our construction, original ciphertexts and re-encryption ciphertexts have the same form, thus only one decryption algorithm is needed for both kinds of ciphertexts. We formalize its security model and prove that it is selective secure under the LWE assumption.