My understanding of PQC (Post Quantum Cryptography) schemes is that they typically require one or more of the following:
- very large public keys
- very large signatures
- very slow validation time
This would dramatically reduce blockchain throughput, if we wish to hold node validation resources constant (i.e. not increase the block size and not allow worst case block validation time to increase significantly).
In addition, the (hardware) wallets that produce such signatures may have to be more powerful, but I’m not concerned about that here.
At the same time there’s much excitement about ZKPs (Zero Knowledge Proofs) in that they are potentially space efficient and cheap to verify.
Both PQC and ZKP require future soft forks to make them practical for individual use.
This begs the question whether you can combine these. If Bitcoin were to have a soft fork that makes ZKP practical, either with a direct op code or through efficient covenant support, can that be used to implement PQC?
I can imagine at least two caveats:
- the choice of ZKP adds an additional cryptographic assumption
- if the ZKP (covenant) is challenge-response based, the worst case footprint would still be a problem
But is that all?
