1) Already have a leader "Dealer"
2) The leader builds a K-of-N set of shared secret keys.
3) They publish a mapping of each participant (participant_i->hash(secret_i))
4) The leader transmits each key to each participant
5) Participants exchange secrets pairwise, armed with the upfront mapping of participants->secrets
6) Select K and a k-of-N secret scheme such that a majority of participants now have a shared key
lots of the claims aren't meaningful:
- "post quantum" for example isn't a special value in this situation.
- "minimal use of cryptography" isn't relevant to practicality
- The "experimental" component doesn't meaningful contribute to the conclusion.
- No public-key-encryption really means "outsource sender identification to the network layer"
- They pretend using a system of equations to solve for a shared key isn't"cryptography".
In general the contribution of the paper reads as "offusicated". The lack of "public key cryptography" sets them up for a novel problem to solve, but it is an arbitrary handicap that doesn't provide utility.
This is academic "make up a novel and nontrivial problem and then solve it", its of utility to the process of producing grad students and publication count but not something we need to get excited about. Read it like a survey paper of the space, which it does well as.