Path validation has been explored as an indispensable security feature for the future Internet. Motivated by the Path-Aware Networking Research Group (PANRG) under the Internet Engineering Task Force (IETF) and Internet Research Task Force (IRTF), it gives end-hosts more control over packet forwarding and ensures that the forwarding history is verifiable. The main idea is to require that routers add proofs in packet headers for other routers to verify. We identify linear-scale proofs as the essential efficiency barrier of existing path validation solutions. In this paper, we propose Atomos to validate network paths with constant-size proofs. To this end, we construct a noncommutative homomorphic asymmetric-key encryption scheme. Asymmetric cryptography minimizes the number of proofs needed and saves time in processing proofs. The homomorphism we design yields constant-size proofs. It limits the header-space overhead and outperforms existing linear-scale counterparts when the path length exceeds a value that is usually small. Furthermore, the proposed encryption scheme is noncommutative so that any deviation from the forwarding path can be detected. We explore a series of design strategies for security and efficiency. The evaluation results show that Atomos yields not only shorter proofs but also faster validation than existing solutions.
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