A membership matrix μ records the hashed contributions used to derive subgroup membership keys. Each node computes one column from the aggregate public-key value A, its public value a_j, and private key ψ_j, then distributes that column to the other nodes. section 18.5
The implementation follows this flow:
- Compute a_jψ_j modulo the system torsion value. section 18.5
- Hash A together with each row index i using H₂(A, i), then multiply every resulting point by a_jψ_j. section 18.5
- For more than ten nodes, replace the (N−1)² peer transfers with collection and redistribution through a central server, reducing communication to 2N transmissions. section 18.5
