Network Coding-Based Post-Quantum Cryptography for Multi-Users with Different Security Permissions

We present a novel multi-legitimate-users hybrid universal network-coding cryptosystem which provides secure Post-Quantum (PQ) cryptography at high communication rates for users with varying levels of data access permission. In previous work, which considered only a single legitimate user network, it was shown how to combine an information-theoretically secure encoder together with partial encryption to obtain PQ security guarantees, even in the presence of an all-observing eavesdropper. This construction was called HUNCC. We provide a new hybrid PQ cryptosystem for broadcast setting, calling it B-HUNCC. Specifically, we consider a scenario in which there are two sets of messages: public messages, which must be available to all legitimate 'restricted and unrestricted' users in the noiseless network, and confidential messages, which must be available only to unrestricted users with appropriate access permission and hidden from other users in the multi-path noiseless network. Under this multi-legitimate-user setting, we provide an efficient hybrid solution: i) A capacity-achieving individually secure broadcast coding scheme that guarantees individual information-theoretic security for restricted users who can select to obtain any subset of the links and ii) a PQ cryptosystem that, by post-encrypting a small part of the transmitted data, guarantees individual indistinguishability under chosen ciphertext attack (individual IND-CCA1) against restricted users who may obtain the entirety network's links but without appropriate access permission, at high information rates.