secret-sharing (empty) → 1.0.0.0

raw patch · 8 files changed

+834/−0 lines, 8 filesdep +QuickCheckdep +basedep +binarysetup-changed

Dependencies added: QuickCheck, base, binary, bytestring, dice-entropy-conduit, finite-field, polynomial, test-framework, test-framework-quickcheck2, vector

Files

• LICENSE +508/−0
• Setup.hs +2/−0
• secret-sharing.cabal +69/−0
• src/Crypto/SecretSharing.hs +36/−0
• src/Crypto/SecretSharing/FiniteField.hs +34/−0
• src/Crypto/SecretSharing/Internal.hs +127/−0
• src/Crypto/SecretSharing/Prime.hs +17/−0
• tests/Tests.hs +41/−0

@@ -0,0 +1,508 @@+Copyright 2008-2009, Peter Robinson <thaldyron@gmail.com>. All rights reserved.++          GNU LESSER GENERAL PUBLIC LICENSE+               Version 2.1, February 1999++ Copyright (C) 1991, 1999 Free Software Foundation, Inc.+ 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA+ Everyone is permitted to copy and distribute verbatim copies+ of this license document, but changing it is not allowed.++[This is the first released version of the Lesser GPL.  It also counts+ as the successor of the GNU Library Public License, version 2, hence+ the version number 2.1.]++                Preamble++  The licenses for most software are designed to take away your+freedom to share and change it.  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@@ -0,0 +1,2 @@+import Distribution.Simple+main = defaultMain

@@ -0,0 +1,69 @@+name:                secret-sharing+version:             1.0.0.0+synopsis:            Information-theoretic secure secret sharing +description:+ 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 data"+ >> shares <- encode 3 5 secret+ >> mapM_ (Prelude.putStrLn . show) shares+ > (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.+license:             LGPL-2.1+license-file:        LICENSE+author:              Peter Robinson <peter.robinson@monoid.at>+maintainer:          peter.robinson@monoid.at+copyright:           Peter Robinson 2014+category:            Cryptography +build-type:          Simple+cabal-version:       >=1.8+homepage:            http://monoid.at/code+tested-with:         GHC==7.8.3+stability:           experimental++library+  hs-source-dirs:    src+  exposed-modules:   Crypto.SecretSharing+                     Crypto.SecretSharing.Internal+                     Crypto.SecretSharing.FiniteField+                     Crypto.SecretSharing.Prime++  build-depends:    base ==4.6.*,+                    bytestring ==0.10.*,+                    dice-entropy-conduit >= 1.0.0.0,+                    binary >=0.5.1.1,+                    vector >=0.10.11.0,+                    finite-field >=0.8.0,+                    polynomial >= 0.7.1+  ghc-options:      -Wall +++test-suite Main+  type:            exitcode-stdio-1.0+  x-uses-tf:       true+  build-depends:   base >= 4 && < 5,+                   QuickCheck >= 2.4,+                   test-framework >= 0.4.1,+                   test-framework-quickcheck2+  hs-source-dirs:  src, tests+  main-is:         Tests.hs+

@@ -0,0 +1,36 @@+-----------------------------------------------------------------------------+-- |+-- Module      :  Crypto.SecretSharing+-- Copyright   :  Peter Robinson 2014+-- License     :  LGPL+-- +-- Maintainer  :  Peter Robinson <peter.robinson@monoid.at>+-- Stability   :  stable+-- Portability :  portable+-- +-- 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 perfect secrecy in the sense that the knowledge of up+-- to @m-1@ shares does not reveal any information about the secret @b@.+--+-- Typically, there are @n@ parties and we would like to give the @i@-th party+-- the @i@-share of each byte. +-- For example, to encode a bytestring @secret@ as @10@ shares, any @5@ of which+-- are sufficient for reconstruction we could write:+--+-- > shares <- encode 5 10 secret+--+-- Note that each byte is encoded separately using a fresh set of random+-- coefficients.+--+-- The mathematics behind the secret sharing scheme is described in:+-- \"How to share a secret.\" by Shamir, Adi.+-- In Communications of the ACM 22 (11): 612–613, 1979.+-- +--+-----------------------------------------------------------------------------++module Crypto.SecretSharing( encode, decode, Share )+where+import Crypto.SecretSharing.Internal

@@ -0,0 +1,34 @@+{-# LANGUAGE DeriveDataTypeable, DeriveGeneric, GeneralizedNewtypeDeriving, TemplateHaskell #-} +-----------------------------------------------------------------------------+-- |+-- Module      :  Crypto.SecretSharing.FiniteField+-- Copyright   :  Peter Robinson 2014+-- License     :  LGPL+-- +-- Maintainer  :  Peter Robinson <peter.robinson@monoid.at>+-- Stability   :  stable+-- Portability :  portable+-- +-----------------------------------------------------------------------------++module Crypto.SecretSharing.FiniteField+where++import Data.Typeable+import GHC.Generics+import Data.FiniteField.PrimeField as PF+import Crypto.SecretSharing.Prime+++-- | A finite prime field. All computations are performed in this field.+newtype FField = FField { number :: $(primeField $ fromIntegral prime) }+  deriving(Show,Read,Ord,Eq,Num,Fractional,Generic,Typeable)+  ++-- | A polynomial over the finite field given as a list of coefficients.+type Polyn = [FField] ++-- | Evaluates the polynomial at a given point.+evalPolynomial :: Polyn -> FField -> FField+evalPolynomial coeffs x +  = foldr (\c res -> c + (x * res)) 0 coeffs

@@ -0,0 +1,127 @@+{-# LANGUAGE DeriveDataTypeable, DeriveGeneric, GeneralizedNewtypeDeriving #-} +-----------------------------------------------------------------------------+-- |+-- Module      :  Crypto.SecretSharing.Internal+-- Copyright   :  Peter Robinson 2014+-- License     :  LGPL+-- +-- Maintainer  :  Peter Robinson <peter.robinson@monoid.at>+-- Stability   :  stable+-- Portability :  portable+-- +-----------------------------------------------------------------------------++module Crypto.SecretSharing.Internal+where+import Math.Polynomial.Interpolation++import Data.ByteString.Lazy( ByteString )+import qualified Data.ByteString.Lazy as BL+import qualified Data.ByteString.Lazy.Char8 as BLC+import qualified Data.List as L+import Data.Maybe+import Data.Char+import Data.Vector( Vector )+import qualified Data.Vector as V+import Data.Typeable+import Control.Exception+import Control.Monad+import Data.Binary( Binary )+import GHC.Generics+import Data.FiniteField.PrimeField as PF++import Crypto.SecretSharing.FiniteField+import Crypto.SecretSharing.Prime+import System.Random.Dice++++-- | A share of an encoded byte. +data ByteShare = ByteShare +  { shareId :: !Int                  -- ^ the index of this share +  , reconstructionThreshold :: !Int  -- ^ number of shares required for +                                     -- reconstruction+  , shareValue :: !Int        -- ^ the value of p(shareId) where p(x) is the +                              --   generated (secret) polynomial+  }+  deriving(Typeable,Eq,Generic)++instance Show ByteShare where+  show = show . shareValue ++-- | A share of the encoded secret.+data Share = Share +  { theShare :: ![ByteShare] }+  deriving(Typeable,Eq,Generic)++instance Show Share where+  show s = show (shareId $ head $ theShare s,BLC.pack $ map (chr . shareValue) $ theShare s)++instance Binary ByteShare+instance Binary Share++-- | Encodes a 'ByteString' as a list of n shares, m of which are required for+-- reconstruction.+-- Lives in the 'IO' to access a random source.+encode :: Int         -- ^ m +       -> Int         -- ^ n+       -> ByteString  -- ^ the secret that we want to share+       -> IO [Share] -- a list of n-shares (per byte) +encode m n bstr +  | n >= prime || m > n = throw $ AssertionFailed $ +      "encode: require n < " ++ show prime ++ " and m<=n."+  | BL.null bstr = return []+  | otherwise = do+  let bytes = map fromIntegral $ BL.unpack bstr+  let len = max 1 ((length bytes) * (m-1))+  coeffs <- (groupInto (m-1) . map fromIntegral . take len ) +                            `liftM` (getDiceRolls prime len)+  let byteVecs = zipWith (encodeByte m n) coeffs bytes+  return [ Share $ map (V.! (i-1)) byteVecs | i <- [1..n] ]+++-- | Reconstructs a (secret) bytestring from a list of (at least @m@) shares. +-- Throws 'AssertionFailed' if the number of shares is too small.+decode :: [Share]    -- ^ list of at least @m@ shares+       -> ByteString -- ^ reconstructed secret+decode []     = BL.pack []+decode shares@((Share s):_) +  | length shares < reconstructionThreshold (head s) = throw $ AssertionFailed +      "decode: not enough shares for reconstruction."+  | otherwise =+    let origLength = length s in+    let byteVecs = map (V.fromList . theShare) shares in+    let byteShares = [ map ((V.! (i-1))) byteVecs | i <- [1..origLength] ] in+    BL.pack . map (fromInteger . PF.toInteger . number) +            . catMaybes . map decodeByte $ byteShares+    ++encodeByte :: Int -> Int -> Polyn -> FField -> Vector ByteShare+encodeByte m n coeffs secret = +  V.fromList[ ByteShare i m $ fromInteger . PF.toInteger . number $ +                evalPolynomial (secret:coeffs) (fromIntegral i::FField) +            | i <- [1..n] +            ]+++decodeByte :: [ByteShare] -> Maybe FField+decodeByte ss =+  let m = reconstructionThreshold $ head ss in+  if length ss < m+    then Nothing+    else+      let shares = take m ss in +      let pts = map (\s -> (fromIntegral $ shareId s,fromIntegral $ shareValue s)) shares in+      Just $ polyInterp pts 0+++-- | Groups a list into blocks of certain size. Running time: /O(n)/+groupInto :: Int -> [a] -> [[a]]+groupInto num as+  | num < 0  = throw $ AssertionFailed "groupInto: Need positive number as argument."+  | otherwise = +    let (fs,ss) = L.splitAt num as in+    if L.null ss +      then [fs]+      else fs : groupInto num ss +

@@ -0,0 +1,17 @@+-----------------------------------------------------------------------------+-- |+-- Module      :  Crypto.SecretSharing.Prime+-- Copyright   :  Peter Robinson 2014+-- License     :  LGPL+-- +-- Maintainer  :  Peter Robinson <peter.robinson@monoid.at>+-- Stability   :  stable+-- Portability :  portable+-- +-----------------------------------------------------------------------------++module Crypto.SecretSharing.Prime( prime )+where+-- | Determines the size of the finite field and the maximum number of shares.+prime :: Int+prime = 1021

@@ -0,0 +1,41 @@+module Main+where+import Data.Monoid+import Test.Framework+import Test.Framework.Providers.QuickCheck2+import Test.QuickCheck+import Data.Maybe+import qualified Data.List as L+import Control.Monad++import Data.ByteString.Lazy( ByteString )+import qualified Data.ByteString.Lazy as B++import Crypto.SecretSharing.Internal+import Crypto.SecretSharing.FiniteField+import Crypto.SecretSharing.Prime++instance Arbitrary ByteString where+    arbitrary   = fmap B.pack arbitrary++main :: IO ()+main = defaultMainWithOpts+       [ testProperty "encodingDecoding" propEncodingDecoding+       ] mempty++data ShareIdxs = ShareIdxs { shareIdxs :: [Int] }+  deriving (Show,Eq,Ord)+ +instance Arbitrary ShareIdxs where+  arbitrary = +    liftM (ShareIdxs . L.nub) $ sequence [ choose (1,prime-1) +                                         | i <- [1..(prime-1) `div` 2]]++propEncodingDecoding bstr idxs = ioProperty $ do+  shares <- encode 20 (prime-1) bstr +  if null shares && B.null bstr+    then return True+    else do+      let chosen = [ shares !! (i-1) | i <- shareIdxs idxs ]  +      return (bstr == (decode chosen)) +