Rhqc: Post-Quantum Ratcheted Key Exchange From Coding Assumptions

Key Exchange mechanisms (KE or KEMs) such as the Diffie-Hellman protocol have proved to be a cornerstone conciliating the efficiency of symmetric encryption and the practicality of public key primitives. Such designs however assume the non-compromission of the long term asymmetric key in use. To relax this strong security assumption, and allow for modern security features such as Perfect Forward Secrecy (PFS) or Post Compromise Security (PCS), Ratcheted-KE (RKE) have been proposed. This work proposes to turn the Hamming Quasi-Cyclic (HQC) cryptosystem into such a Ratcheted-KE, yielding the first code-based such construction. Interestingly, our design allows indifferently one party to update the key on-demand rather than the other, yielding a construction called bi-directionnal RKE, which compares favorably to generic transformations. Finally, we prove that the resulting scheme satisfies the usual correctness and key-indistinguishability properties, and suggest concrete sets of parameters, assuming different reallife use cases.