Resharing Shamir Secret Shares to Change the Threshold

A deep dive into verifiable secret resharing (VSR) for Shamir Secret Sharing groups, explaining how to recompute shares with a new threshold without revealing the underlying secret. The protocol uses multi-party computation with polynomial interpolation and elliptic curve commitments to ensure correctness even with malicious participants. Covers the full step-by-step resharing protocol, verification via public coefficient commitments, and practical use cases including revoking exposed shares, replacing shareholders, changing thresholds, and defending against mobile adversaries who steal shares incrementally over time. Also discusses gotchas like share compatibility fragmentation and the difficulty of enforcing threshold increases.