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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);; |
And also, the checksum let me encrypt the pieces in an internal format (for example, JSON) and then validate against corrupted data during traffic.
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.
The checksum also enables the brute-force of the message, only if fewer parts are missing due "shareholders" dropping the game in the middle. It possibly will only be feasible in some sense if the threshold is 90%, I guess - I should make a Proof-of-Concept for that...