I am looking for a references for post-quantum threshold secret sharing schemes.
I am especially interested in knowing whether any one based on one-way compressor functions or cryptographic hashes exist.
The trivial secret sharing systems with $t=1$ and $t=n$ give information-theoretic security.
Here are some other alternatives that I don't know the security of:
- Shamir's secret sharing - I don't know [Update: gives information-theoretic security]
- Blakley's scheme - I don't know
- The Chinese Remainder Theorem - It seems like it is a problem a quantum computer would easily solve.