Module recovery 

Share backup + recovery for CMP20 threshold shares.

If a custodian loses their share, any T of the remaining N-1 shares can reconstruct the lost share’s scalar value without revealing it to any single party.

Protocol

1. Each of T remaining parties computes a Lagrange interpolation of their share at the lost party’s x-coordinate.
2. Combiner sums the T partial recoveries.
3. The result is the lost share’s scalar — assign it to the replacement custodian.
4. No change to the joint public key.

The math is identical to [crate::keygen::reconstruct_secret_for_test] but evaluated at the lost party’s x instead of x=0.

Enums

RecoverError

Errors during share recovery.

Functions

recover_share

Recover a full Cmp20Share (scalar + public key + party index) from T surviving shares. The public key is taken from any surviving share (they all carry the same joint public key).

recover_share_scalar

Recover a lost share’s scalar value from T surviving shares.