As Large Language Model (LLM) agents emerge as intelligent coordinators, they intensify the demand for secure sharing and forwarding of sensitive data in data-driven systems. Existing Attribute-Based Proxy Re-Encryption (ABPRE) offers fine-grained access control and secure data forwarding, but suffers from the key escrow problem and lacks efficient verifiability and fairness guarantees. In this paper, we propose the first Verifiable and Fair Registered ABPRE (VF-RABPRE) scheme to eliminate reliance on trusted authorities and support multi-hop re-encryption for flexible multi-agent data sharing. To ensure efficient verifiability and fairness, we combine a lightweight verifiable tag and a non-interactive zero-knowledge proof to detect misbehavior of the proxy and prevent false accusations. As a trade-off between security and overhead, we design a more secure fairness mechanism that does not reveal plaintext using zero-knowledge Succinct Non-interactive Arguments of Knowledge (zkSNARK). Additionally, we extend VF-RABPRE with dynamic user registration and outsourced decryption, supporting flexible registration and efficient decryption for data users. Finally, we formally prove the security of our scheme and implement a prototype to evaluate its performance. Experimental results demonstrate that VF-RABPRE outperforms state-of-the-art ABPRE schemes and achieves practical efficiency, making it well-suited for secure data sharing in scenarios empowered by LLM agents.

Proximity testing for linear codes is a fundamental problem in coding theory with critical applications in cryptographic protocols, blockchain, and distributed storage systems. This work addresses the proximity gaps for linear codes, a crucial aspect for efficiently verifying whether a batch of words is close to a given code. We present a general framework for deriving proximity gaps from the list-decodability properties of the underlying linear code. Our main result show that for any (p,L)-list-decodable codeC⊆ Fnqwith minimum relative distance ΔC>p, the probability that a random combination of a batch of t words containing a δ-far word (for δ ≤ 1 − √ 1 −p+ ε) remains δ-far fromCis bounded byO(tL2pn/q+t/εq). This result also establishes a form of (mutual) correlated agreement for linear codes, which can be used to strengthen soundness analyses in protocols that rely on proximity testing, thereby reducing query complexity and enabling practical instantiations over smaller finite fields. In particular, we apply our main result to randomly punctured Reed–Solomon codes and folded Reed–Solomon codes—both of which are known to achieve list-decodability up to capacity—and derive linear proximity gaps for these families of codes under the Johnson bound.