Proof that a participant has really shared private key with SSSS

[dr-orlovsky]

Proposed scheme is based on probabilistic checkable proof and runs as follows:

1. Upon secret sharing of a private key compute a deterministic random oracle by performing binary xor operation for all secret parts and computing RIPEMD160 hash function of the result.
2. Define an order of the shared secrets by computing the modulo from the division of its value by the hash - and sort secrets in ascending order.
3. Run a secret restoration algorithm on the ordered set of shares, organize intermediate results into an ordered sequence.
4. Compute Merkle tree and run PCP with this sequence.