Expanded Shamir's Secret Sharing

Use the thing

import com.codahale.shamir.ExpandedScheme;
import java.nio.charset.StandardCharsets;
import java.util.Map;

class Example {
  void doIt() {
    final ExpandedScheme scheme = ExpandedScheme.of(5, 1, 3);
    final byte[] secret = "hello there".getBytes(StandardCharsets.UTF_8);
    final Map<Integer, byte[]> parts = scheme.split(secret);
    final byte[] recovered = scheme.join(parts);
    System.out.println(new String(recovered, StandardCharsets.UTF_8));
  } 
}

How it works

Expanded Secret Sharing allows to split secret S into N parts, of which M are mandatory to reconstruct S and K-M are optional in the recovery process. Mandatory parts ID is always between 1 and M. Optional parts ID is always greater than M.

Example:

Password must be split between one admin and four users and to recover it, admin and at least any two of users must combine their parts. In this particular case, ExpandedScheme[n=5, m=1, k=3] is needed. Part with ID 1 should be given to admin and the rest can be randomly distributed between users.

Implementation details

Expanded Secret Sharing uses original Coda Hale's split and join operations implementations, just twice. Firstly, secret is splited into M+1 parts, of which all are needed for reconstruction process. Parts with ID from 1 to M are the mandatory parts. Secondly, M+1 part is splited into M-K optional parts with IDs between M+1 and K. K-M optional parts are needed to reconstruct a part from previous split. This approach ensures that any K or more parts must include all of M mandatory parts to retrieve the original secret.

License

Copyright © 2018 Balciu

Distributed under the Apache License 2.0.