secret-sharing: Information-theoretic secure secret sharing

Implementation of an (m,n)-threshold secret sharing scheme. A given ByteString b (the secret) is split into n shares, and any m shares are sufficient to reconstruct b. The scheme preserves information-theoretic perfect secrecy in the sense that the knowledge of up to m-1 shares does not reveal any information about the secret b.

Example in GHCi: Suppose that you want to split the string "my secret data" into n=5 shares such that at least m=3 shares are necessary to reconstruct the secret.

> :m + Data.ByteString.Lazy.Char8 Crypto.SecretSharing
> let secret = pack "my secret message!"
> shares <- encode 3 5 secret
> mapM_ (Prelude.putStrLn . show) shares -- each share should be deposited at a different site.
 (1,"\134\168\154\SUBV\248\CAN:\250y<\GS\EOT*\t\222_\140")
 (2,"\225\206\241\136\SUBse\199r\169\162\131D4\179P\210x")
 (3,"~\238%\192\174\206\\\f\214\173\162\148\&3\139_\183\193\235")
 (4,"Z\b0\188\DC2\f\247\f,\136\&6S\209\&5\n\FS,\223")
 (5,"x\EM\CAN\DELI*<\193q7d\192!/\183v\DC3T")
> let shares' = Prelude.drop 2 shares
> decode shares'
 "my secret message!"

The mathematics behind the secret sharing scheme is described in: "How to share a secret." by Adi Shamir. In Communications of the ACM 22 (11): 612–613, 1979.

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