International Association
for Cryptologic Research

Proxy re-encryption (PRE) allows a proxy to transform a ciphertext intended for Alice (delegator) to another ciphertext intended for Bob (delegatee) without revealing the underlying message. Recently, a new variant of PRE, namely fine-grained PRE (FPRE), was proposed in [Zhou et al., Asiacrypt 2023]. Generally, FPRE is designed for a function family F: each re-encryption key rk_{A→B}^f is associated with a function f ∈ F, and with rk_{A→B}^f, a proxy can transform Alice's ciphertext encrypting m to Bob's ciphertext encrypting f(m). However, their scheme only supports single-hop re-encryption and achieves only CPA security.

In this paper, we formalize multi-hop FPRE (mFPRE) that supports multi-hop re-encryptions in the fine-grained setting, and propose two mFPRE schemes achieving CPA security and stronger HRA security (security against honest re-encryption attacks), respectively. -- For multi-hop FPRE, we formally define its syntax and formalize a set of security notions including CPA security, HRA security, undirectionality and ciphertext unlinkablity. HRA security is stronger and more reasonable than CPA security, and ciphertext unlinkablity blurs the proxy relations among a chain of multi-hop re-encryptions, hence providing better privacy. We establish the relations between these security notions. -- Our mFPRE schemes support fine-grained re-encryptions for bounded linear functions and have security based on the learning-with-errors (LWE) assumption in the standard model. In particular, one of our schemes is HRA secure and enjoys all the aforementioned desirable securities. To achieve CPA security and HRA security for mFPRE, we extend the framework of [Jafargholi et al., Crypto 2017] and the technique of the [Fuchsbauer et al., PKC 2019].