In cryptography, key establishment protocols are often the starting point paving the way towards secure execution of different tasks. Namely, the parties seeking to achieve some cryptographic task, often start by establishing a common high-entropy secret that will eventually be used to secure their communication. In this paper, we put forward a security model for group key establishment (
GAKE) with an adversary that may execute efficient quantum algorithms, yet only once the execution of the protocol has concluded. This captures a situation in which keys are to be established in the present, while security guarantees must still be provided in the future when quantum resources may be accessible to a potential adversary. Further, we propose a protocol design that can be proven secure in this model. Our proposal uses password authentication and builds upon efficient and reasonably well understood primitives: a message authentication code and a post-quantum key encapsulation mechanism. The hybrid structure dodges potential efficiency downsides, like large signatures, of some “true” post-quantum authentication techniques, making our protocol a potentially interesting fit for current applications with long-term security needs.