Simple Secret Sharing using XOR operation (OCaml example).

secret-sharing.ml

let shuffle list =
  let cmp _ _ = (Random.int 3) - 1 in
  List.sort cmp list;;

let share ~secret ~length =
  let rec loop secret length buffer =
    if length <= 0 then secret :: buffer else
    let noise = Random.bits () in
    let piece = secret lxor noise in
    loop piece (length - 1) (noise :: buffer)
  in
  let pieces = loop secret (length - 1) [] in
  shuffle pieces;;

let recover pieces =
  let op x y = x lxor y in
  let head = List.hd pieces in
  let tail = List.tl pieces in
  List.fold_left op head tail;;

let pieces =
  Random.self_init ();
  share ~secret:23 ~length:10;;

assert (23 = recover pieces);;

UPDATE:

Full code available here: https://github.com/marcoonroad/shareholders

The shares are encrypted using the checksum (of the secret) as the AES CBC key & IV, then HMAC-alike signed with the digest of this secret checksum.

By encrypting the shares, I can add metadata on them, such as their position (i, j) on the random numbers matrix. Such metadata allow me to track missing matrix cells and them brute-force them against the checksum to recover the secret. The implemented redundancy on the library above will help here, 'cause it will reduce the vector space of missing share pieces to brute-force/discover.