HRA-Secure Homomorphic Lattice-Based Proxy Re-Encryption with Tight Security

We construct an efficient proxy re-encryption (PRE) scheme secure against honest re-encryption attacks (HRA-secure) with precise concrete security estimates. To get these precise concrete security estimates, we introduce the tight, fine-grained noise-flooding techniques of Li et al. (CRYPTO'22) to RLWE-based (homomorphic) PRE schemes, as well as a mixed statistical-computational security definition to HRA security analysis. Our solution also supports homomorphic operations on the ciphertexts. Such homomorphism allows for advanced applications, e.g., encrypted computation of network statistics across networks, and unlimited hops in the case of full homomorphism, i.e., when bootstrapping is available. We implement our PRE scheme in the OpenFHE software library and apply it to a problem of secure multi-hop data distribution in the context of 5G virtual network slices. We also experimentally evaluate the performance of our scheme, demonstrating that the implementation is practical. Moreover, we compare our PRE method with other lattice-based PRE schemes and approaches targeting HRA security. These achieve HRA security, but not in a tight, practical scheme such as our work. Further, we present an attack on the PRE scheme proposed in Davidson et al.'s (ACISP'19), which was claimed to achieve HRA security without noise flooding, i.e., without adding large noise.