I am trying to implement a mixnet using post-quantum public-key crypto. Each message may be encrypted by up to 10 levels of public keys, shuffled, before the layers of encryption are stripped off one by one.
This is traditionally achievable in RSA, because the ciphertext is barely larger than the plaintext, but in the many popular post-quantum public key cryptosystems (based on lattice crypto), such as NTRU, it appears the ciphertext becomes an order of magnitude larger than the plaintext. So encapsulating a message in multiple layers of encryption is infeasible as the ciphertext doesn't scale.
Are there post-quantum public key exchange schemes suitable for this purpose? I've looked at the Open quantum safe project, but am unsure whether any of protocols there mitigate this issue, or are mature enough.