data-dispersal (empty) → 1.0.0.0
raw patch · 8 files changed
+1116/−0 lines, 8 filesdep +AESdep +QuickCheckdep +arraysetup-changed
Dependencies added: AES, QuickCheck, array, base, binary, bytestring, entropy, finite-field, matrix, secret-sharing, spool, syb, test-framework, test-framework-quickcheck2, vector
Files
- LICENSE +508/−0
- Setup.hs +2/−0
- data-dispersal.cabal +132/−0
- src/Crypto/IDA.hs +125/−0
- src/Data/IDA.hs +31/−0
- src/Data/IDA/FiniteField.hs +129/−0
- src/Data/IDA/Internal.hs +137/−0
- tests/Tests.hs +52/−0
+ LICENSE view
@@ -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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+ Setup.hs view
@@ -0,0 +1,2 @@+import Distribution.Simple+main = defaultMain
+ data-dispersal.cabal view
@@ -0,0 +1,132 @@+name: data-dispersal++-- The package version. See the Haskell package versioning policy (PVP) +-- for standards guiding when and how versions should be incremented.+-- http://www.haskell.org/haskellwiki/Package_versioning_policy+-- PVP summary: +-+------- breaking API changes+-- | | +----- non-breaking API additions+-- | | | +--- code changes with no API change+version: 1.0.0.0++synopsis: Space-efficient and privacy-preserving data dispersal algorithms.++description:+ This library provides space-efficient (m,n)-information dispersal algorithms (IDAs). + .+ Given a ByteString @bstr@ of length @D@, we encode @bstr@ as a list @fs@ of @n@ + 'Fragment's, each containing a ByteString+ of length @O(D/m)@. Then, each fragment in @fs@ could be stored on a separate + machine for fault-tolerance.+ Even if up to @n-m@ of these machines crash, we can still reconstruct the original + ByteString out of the remaining m fragments.+ The total space required for the n fragments is @O((n/m)*D)@.+ Note that @m@ and @n@ are roughly in the same order, so the actual storage overhead + for getting good fault-tolerance increases only by a constant factor.+ .+ The module @Data.IDA@ contains the basic information dispersal algorithm. The module+ @Crypto.IDA@ augments the dispersal scheme by combining it with secret sharing, i.e.,+ the knowledge of up to @m-1@ fragments does not leak any information about+ the original data. See "Crypto.IDA" for details.+ .+ /GHCi Example:/+ .+ > > :m + Data.IDA+ > > let msg = Data.ByteString.Char8.pack "my really important data"+ > > let fragments = encode 5 15 msg+ > -- Now we could distributed the fragments on different sites to add some + > -- fault-tolerance.+ > > let frags' = drop 5 $ take 10 fragments -- let's pretend that 10 machines crashed+ > > decode frags' + > "my really important data"+ .+ /Fault-Tolerance:/+ .+ Suppose that we have @N@ machines and encode our data as @2log(N)@ fragments + with reconstruction threshold m = @log(N)@.+ Let's assume that we store each fragment on a separate machine and each+ machine fails (independently) with probability at most 0.5.+ .+ * What is the probability of our data being safe? + @Pr[ at most n-m machines crash ] >= 1-0.5^(log(N)) = 1-N^(-1).@+ .+ * What is the overhead in terms of space that we pay for this level of fault-tolerance?+ We have n fragments, each of size D\/m, so the total space is @n * D\/ m = + 2D.@+ In other words, we can guarantee that the data survives with high probability + by increasing the required space by a constant factor.+ .+ This library is based on the following works: + .+ * \"Efficient Dispersal of+ Information for Security, Load Balancing, and Fault Tolerance\", by Michael O.+ Rabin, JACM 1989.+ .+ * \"How to share a secret.\" by Adi Shamir.+ In Communications of the ACM 22 (11): 612–613, 1979.+ .+ * \"Secret Sharing Made Short\" Hugo Krawczyk.+ CRYPTO 1993: 136-146+++license: LGPL-2.1++license-file: LICENSE++author: Peter Robinson <peter.robinson@monoid.at>++maintainer: peter.robinson@monoid.at++copyright: Peter Robinson 2014++category: Data, Cryptography++build-type: Simple++cabal-version: >=1.8++homepage: http://monoid.at/code+++library+ hs-source-dirs: src++ exposed-modules: Data.IDA + Data.IDA.Internal+ Data.IDA.FiniteField+ Crypto.IDA++ build-depends: base ==4.6.*+ ,array >= 0.4.0.1+ ,vector >= 0.10.11.0+ ,binary >= 0.7.2.1+ ,bytestring >= 0.10.0.2+ ,syb >= 0.4.0+ ,binary >= 0.5.1.1+ ,finite-field >= 0.8.0+ ,matrix >= 0.3.4.0+ ,AES >= 0.2.9+ ,entropy >= 0.3.2+ ,secret-sharing >= 1.0.0.0+ + 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+ ,array >= 0.4.0.1+ ,vector >= 0.10.11.0+ ,spool >= 0.1+ ,binary >= 0.7.2.1+ ,bytestring >= 0.10.0.2+ ,syb >= 0.4.0++ hs-source-dirs: src, tests++ main-is: Tests.hs+
+ src/Crypto/IDA.hs view
@@ -0,0 +1,125 @@+-----------------------------------------------------------------------------+-- |+-- Module : Crypto.IDA+-- Copyright : Peter Robinson 2014+-- License : LGPL+-- +-- Maintainer : Peter Robinson <peter.robinson@monoid.at>+-- Stability : experimental+-- Portability : portable+--+-- This module provides an (m,n)-information dispersal scheme that provides+-- data redundancy while preserving secrecy. +-- In other words, this module combines the best of 2 worlds: secret sharing+-- algorithms with low-overhead information dispersal.+-- +-- Function 'encode' splits a given bytestring into @n@ fragments with the +-- following properties:+--+-- 1. Any @m@ of the @n@ fragments are sufficient for reconstructing the original+-- bytestring via 'decode', and+-- 2. the knowledge of up to @m-1@ fragments does /not/ reveal any information+-- about the original bytestring.+--+--+-- In more detail, suppose that we have some bytestring @b@ that we want to +-- (securely) disperse and parameter @m@, @n@.+-- Running 'encode' @m n b@ does the following: +--+-- * Generate a randomly chosen key of 32 bytes, called @key@.+-- * Encrypt the bytestring @b@ using @key@ via AES.+-- * Generate @n@ shares using the perfect secret sharing algorithm implemented +-- in module "Crypto.SecretSharing"; see package <http://hackage.haskell.org/package/secret-sharing>secret-sharing+-- * Generate @n@ fragments of the encrypted data using the information +-- dispersal algorithm in "Data.IDA".+-- * Finally, we pair up these shares and fragments as +-- a list of 'EncryptedFragment's. +--+-- The size of each encrypted fragment is @O(|b|\/m + |key|)@.+-- For sufficiently large bytestrings, the @O(|b|\/m)@ factor dominates and thus+-- the scheme is space-optimal.+--+-- The secret sharing algorithm guarantess that the knowledge of up to @m-1@ of +-- the fragments does not leak any information about the encryption key (and +-- hence the encrypted data). +--+-----------------------------------------------------------------------------+{-# LANGUAGE DeriveDataTypeable, ScopedTypeVariables, DeriveGeneric #-}+module Crypto.IDA( EncryptedFragment(fragmentId,keyShare,aesIV,fragment)+ , encode+ , decode+ )+where+import Data.IDA.Internal( Fragment(..) )+import qualified Data.IDA.Internal as IDA++import Crypto.SecretSharing( Share )+import qualified Crypto.SecretSharing as PSS++import Data.ByteString.Lazy( ByteString )+import qualified Data.ByteString.Lazy as BL+import qualified Data.ByteString as B+import System.Entropy( getEntropy )+import Codec.Crypto.AES +import Control.Exception+import Data.Typeable+import Data.Binary( Binary )+import GHC.Generics++data EncryptedFragment = EncryptedFragment+ { fragmentId :: Int -- ^ the id of the encrypted fragment, ranging from 1 to n.+ , keyShare :: Share -- ^ the list of (bytewise) shares of the AES key+ , aesIV :: B.ByteString -- ^ the initialization vector of the AES encryption+ , fragment :: Fragment -- ^ the encrypted fragment of the original data+ }+ deriving(Typeable,Show,Eq,Generic)++instance Binary EncryptedFragment+++aesKeyLength, aesIVLength :: Int+aesKeyLength = 32+aesIVLength = 16++-- | Space efficient and secrecy-preserving (m,n)-information dispersal: +-- Generates @n@ fragments out +-- of a given bytestring @b@. Each fragment has size @length b \/ m + O(1)@.+-- At least m fragments are required for reconstruction.+-- Preserves secrecy: Assuming that these fragments are distributed +-- among different sites, the knowledge of less than m +-- fragments provides /no/ information about the original data whatsoever.+encode :: Int -- ^ m: number of fragments required for reconstruction+ -> Int -- ^ n: total number of fragments (@n ≥ m@)+ -> Maybe ByteString -- ^ the initialization vector for the AES encryption+ -> ByteString -- ^ the information that we want to disperse+ -> IO [EncryptedFragment] -- ^ a list of n encrypted fragments.+encode m numFragments mIV msg = do+ key <- getEntropy aesKeyLength+ iv <- maybe (getEntropy aesIVLength) (return . BL.toStrict) mIV+ keyShareList <- PSS.encode m numFragments (BL.fromStrict key)+ let headers = zip keyShareList (replicate numFragments $ BL.fromStrict iv)+ let fs = IDA.encode m numFragments $ BL.toStrict $ crypt CTR key iv Encrypt msg+ return [ EncryptedFragment i ks (BL.toStrict iv) f + | (i,(ks,iv),f) <- zip3 [1..] headers fs + ]+ +-- | Reconstruct the original data from (at least) @m@ fragments.+-- Throws an 'AssertionFailed' exception if an insufficient number fragments are+-- given or if a decoding error occurs.+decode :: [EncryptedFragment] + -> ByteString+decode [] = BL.pack []+decode pss@(p:_) + | length pss < IDA.reconstructionThreshold (fragment p) = throw $ AssertionFailed + "decode: not enough fragments for reconstruction."+ | otherwise =+ let m = IDA.reconstructionThreshold $ fragment p in+ let efs = take m pss in+ let iv = aesIV p in+ let fs = map fragment efs in+ let ss = map keyShare efs in+ let emsg = IDA.decode fs in+ let key = PSS.decode ss in+ crypt CTR (BL.toStrict key) iv Decrypt $ BL.fromStrict emsg++
+ src/Data/IDA.hs view
@@ -0,0 +1,31 @@+-----------------------------------------------------------------------------+-- |+-- Module : Data.IDA+-- Copyright : Peter Robinson 2014+-- License : LGPL+-- +-- Maintainer : Peter Robinson <peter.robinson@monoid.at>+-- Stability : experimental+-- Portability : portable+-- +-- This module provides an implementation of a space efficient (m,n)-threshold information +-- dispersal algorithm (IDA) as described in +-- "Efficient Dispersal of Information for Security, Load Balancing, and Fault+-- Tolerance", by Michael O. Rabin, JACM 1989.+--+-- Given a ByteString bstr of length D+-- >>> f = encode m n bstr+-- encodes bstr as a list of n 'Fragment's, each containing a ByteString+-- of length approximately @D/m@. For reconstructing the original ByteString out +-- of a sublist fssub of fs, +-- consisting of at least m fragments, use+-- >>> decode fssub+--+-----------------------------------------------------------------------------+module Data.IDA(encode,decode,Fragment(fragmentId))+where+import Data.IDA.Internal++++
+ src/Data/IDA/FiniteField.hs view
@@ -0,0 +1,129 @@+{-# LANGUAGE DeriveDataTypeable, DeriveGeneric, GeneralizedNewtypeDeriving, TemplateHaskell, Haskell2010, TypeFamilies, FlexibleContexts, Trustworthy, FlexibleInstances, TypeSynonymInstances, OverlappingInstances, UndecidableInstances #-}+-----------------------------------------------------------------------------+-- |+-- Module : Data.IDA.FiniteField+-- Copyright : Peter Robinson 2014+-- License : LGPL+-- +-- Maintainer : Peter Robinson <peter.robinson@monoid.at>+-- Stability : experimental+-- Portability : portable+-- +-- Computations in a finite prime field+-- +-----------------------------------------------------------------------------++module Data.IDA.FiniteField +where++import Control.Exception+import Data.Typeable+import GHC.Generics+import qualified Data.FiniteField.PrimeField as PF+import Data.FiniteField.Base+import Data.IDA.Prime++import qualified Data.Vector as V+import Data.Vector(Vector)+import Data.Matrix+import Data.Monoid+import Data.Binary++++-- | Our finite prime field. All computations are performed in this field.+newtype FField = FField { number :: $(PF.primeField $ fromIntegral prime) }+ deriving(Show,Read,Ord,Eq,Num,Fractional,Generic,Typeable,FiniteField)++instance Monoid FField where + mempty = 0+ mappend = (+)+++instance Enum FField where+ toEnum = FField . fromIntegral + fromEnum = fromEnum . PF.toInteger . number++instance Binary FField where+ get = do + n <- get :: Get Integer+ return $ FField { number = fromInteger n }+ put f = put (PF.toInteger $ number f)+++-- | A matrix over the finite field.+type FMatrix = Matrix FField +++dotProduct :: Num a => Vector a -> Vector a -> a+dotProduct v1 v2 = V.sum $ V.zipWith (*) v1 v2+++-- | Solves a linear equality system @A x = b@ given by a lower triangular matrix via+-- forward substitution.+forwardSub :: Fractional a => Matrix a -> Vector a -> Vector a+forwardSub lower bV =+ forwardSub' lower bV (V.empty)+ where+ forwardSub' lower bV xV + | nrows lower == 0 = xV+ | otherwise = + let curRow = getRow 1 lower + offset = V.length xV+ lm = getRow 1 lower V.! offset+ curB = V.head bV + negSum = curRow `dotProduct` xV+ curX = (curB - negSum) / lm+ in+ forwardSub' (submatrix 2 (nrows lower) 1 (ncols lower) lower) + (V.tail bV) + (V.snoc xV curX)+++-- | Solves a linear equality system @A x = b@ given by an upper triangular matrix via+-- backward substitution.+backwardSub :: Fractional a => Matrix a -> Vector a -> Vector a+backwardSub upper bV =+ backwardSub' upper bV V.empty (nrows upper)+ where+ backwardSub' upper bV xV i + | nrows upper == 0 = xV+ | i<=0 = xV+ | otherwise = + let curRow = snd $ V.splitAt i $ getRow i upper + lm = (getRow i upper) V.! (i-1)+ curB = bV V.! (i-1)+ negSum = xV `dotProduct` curRow+ curX = (curB - negSum) / lm+ in+ backwardSub' upper bV (curX `V.cons` xV) (i-1)+ +-- | Compute the inverse of matrix. Throws 'AssertionFailed' if the matrix is+-- not invertible. +inverse :: (Ord a,Fractional a) => Matrix a -> Matrix a+inverse mat = + let mInv = luDecomp mat+ in + case mInv of + Nothing -> throw $ AssertionFailed "inverse: matrix is not invertible!"+ Just (upper,lower,pmatrix,_) -> + let m = nrows mat+ bVecs = [ getCol i (identity m) | i <- [1..m] ]+ columnsOfInverse = flip map bVecs $ \bV ->+ let yV = forwardSub lower (getCol 1 $ pmatrix * colVector bV)+ xV = backwardSub upper yV+ in colVector xV+ in + foldr (<|>) (fromLists [[]]) columnsOfInverse++ +-- | Construct a Vandermonde matrix. The i-th list element is the i-th seed of +-- the geometric progression of the i-th row.+vandermonde :: Int -> [FField] -> FMatrix+vandermonde m is = matrix (length is) m $ \(i,j) -> (fromIntegral i)^(fromIntegral $ j-1)++-- | Create an nxm Vandermonde matrix. /O(n m)/.+vmatrix :: Int -> Int -> FMatrix+vmatrix numFragments m = vandermonde m [1..fromIntegral numFragments]++
+ src/Data/IDA/Internal.hs view
@@ -0,0 +1,137 @@+-----------------------------------------------------------------------------+-- |+-- Module : Data.IDA.Internal+-- Copyright : Peter Robinson 2014+-- License : LGPL+-- +-- Maintainer : Peter Robinson <peter.robinson@monoid.at>+-- Stability : experimental+-- Portability : portable+--+-----------------------------------------------------------------------------+{-# LANGUAGE DeriveDataTypeable, ScopedTypeVariables, DeriveGeneric #-}+module Data.IDA.Internal +where+import Data.ByteString( ByteString )+import qualified Data.ByteString as B+import Data.Vector(Vector,(!))+import qualified Data.Vector as V+import Data.Array( array )+import qualified Data.Array as A+import Control.Exception+import Data.Typeable+import Data.Binary( Binary )+import GHC.Generics+import qualified Data.Matrix as M++import Data.IDA.FiniteField+import qualified Data.FiniteField.PrimeField as PF+++ ++-- | A fragment of the original data.+data Fragment = Fragment + { fragmentId :: !Int -- ^ index of this fragment + , trailLength :: !Int -- ^ number of symbols added to the original message+ , reconstructionThreshold :: !Int -- ^ number of fragments required for reconstruction+ , theContent :: ![FField] -- ^ the encoded content of the fragment+ , msgLength :: !Int -- ^ length of the original message+ }+ deriving(Typeable,Show,Eq,Generic)++instance Binary Fragment+++-- | Takes a message (a bytestring) and yields 'n' fragments such that any 'm' of+-- them are sufficient for reconstructing the original message.+encode :: Int -- ^ m: we need ≥ 'm' fragments to reconstruct the original message+ -> Int -- ^ n: total number of fragments into which we are going to + -- split the message; 'n' ≥ 'm'+ -> ByteString -- ^ the original message+ -> [Fragment] -- ^ 'n' fragments+encode m numFragments msg + | numFragments >= 1021 && numFragments <1 = + throw $ AssertionFailed "encode: invalid number of fragments."+ | otherwise =+ let (intseq,trailLen) = toIntVec m msg + len = V.length intseq + blocks = V.fromList $ groupInto m intseq + vm = vmatrix numFragments m + c i k = dotProduct (M.getRow i vm) (blocks ! (k-1)) -- product M.! (i,k) + content i = [ c i j + | j <- [ 1 .. ceiling $ fromIntegral len / fromIntegral m ]+ ] in+ [ Fragment { fragmentId = i + , trailLength = trailLen + , reconstructionThreshold = m + , theContent = content i + , msgLength = len + } + | i <- [1 .. numFragments]+ ]+ +-- | Takes a list of at least m fragments (where 'm' is the reconstruction +-- threshold used for 'encode') and tries to reconstruct the original message.+-- Throws an 'AssertionFailed' exception if there are less than m fragments+-- or if the fragments belong to a different message.+decode :: [Fragment] + -> ByteString+decode [] = throw $ AssertionFailed + "decode: need at least m fragments for reconstruction."+decode pss@(p:_) + | length pss < reconstructionThreshold p = throw $ AssertionFailed + "decode: need at least m fragments for reconstruction."+ | otherwise =+ let m = reconstructionThreshold p + idxs = map fragmentId (take m pss) + n = maximum idxs + fragments :: [Vector FField]+ fragments = map (V.fromList . theContent) (take m pss)+ idxVec = V.fromList idxs + vecA = M.matrix m m $ \(i,j) -> + vmatrix n m M.! (idxVec!(i-1),j) + matrixBInv = inverse vecA + colVecR :: Vector FMatrix + colVecR = V.fromList + [ M.transpose $ M.fromLists [ map (! (k-1)) fragments ] + | k <- [1..V.length (head fragments)] + ] + idxList = [(j,k) | k <- [1..V.length (head fragments)], j <- [1..m]] + matrixBInvTimesColVecr = array ((1,1),(V.length (head fragments),m)) + [ ((k,j),head $ + array (1,m) (zip [1..] $ M.toLists $ matrixBInv + *+ (colVecR ! (k-1))) A.! j) + | k <- [1..V.length (head fragments)], j <- [1..m]] + mCont :: [FField]+ mCont = map (\(j,k) -> matrixBInvTimesColVecr A.! (k,j)) idxList in+ fromIntVec (msgLength p - trailLength p) $ V.fromList mCont+++-- | Takes an integer m and a bytestring and converts the bytestring into a+-- 'Vector Word8', appending 0s at the end such that the length is dividable by+-- m.+toIntVec :: Int -> ByteString -> (Vector FField,Int)+toIntVec m bStr = + let len = B.length bStr in+ let trailLen = if (len `mod` m) == 0 then 0+ else ((len `div` m)+1)*m - len in + let bStrApp = bStr `B.append` B.pack (replicate trailLen 0) in+ (V.fromList $ map fromIntegral $ B.unpack bStrApp,trailLen)+++-- | Converts a bytestring to a 'Vector Word8', removing the trailing 0s.+fromIntVec :: Int -> Vector FField -> ByteString+fromIntVec originalLength intVec = + B.pack $ map (fromInteger . PF.toInteger . number) $ V.toList $ V.slice 0 originalLength intVec+++-- | Splits a vector into lists of the given size. O(vector-length \/ size).+groupInto :: Int -> Vector a -> [Vector a]+groupInto size as =+ let (fs,ss) = V.splitAt size as in+ if V.null ss + then [fs]+ else fs : groupInto size ss+
+ tests/Tests.hs view
@@ -0,0 +1,52 @@+module Main+where+import Data.Monoid+import Test.Framework+import Test.Framework.Providers.QuickCheck2+import Test.QuickCheck+import Data.Maybe+import GHC.Conc++import qualified Data.ByteString as BS+import qualified Data.ByteString.Lazy as BL+import qualified Data.IDA as IDA+import qualified Crypto.IDA as SecretIDA++instance Arbitrary BS.ByteString where+ arbitrary = fmap BS.pack arbitrary+instance Arbitrary BL.ByteString where+ arbitrary = fmap BL.pack arbitrary++main :: IO ()+main = do + defaultMainWithOpts+ [ testProperty "IDAencodingDecoding" propIDAEncodingDecoding+ , testProperty "SecretIDAencodingDecoding" propSecretIDAEncodingDecoding+ ] mempty ++ ++-- | Input: bytestring b, list of booleans.+-- First, encode b, then randomly select sufficiently many fragments according to+-- the boolean list, finally decode these fragments and check if the original+-- bytestring is matched.+propIDAEncodingDecoding bstr blist = + let frags = IDA.encode 10 40 bstr in+ let chosen = fst $ unzip $ filter snd $ zip frags blist in+ if length chosen < 10 + then True+ else bstr == IDA.decode chosen +++-- | Input: bytestring b, list of booleans.+-- First, encode b, then randomly select sufficiently many fragments according to+-- the boolean list, finally decode these fragments and check if the original+-- bytestring is matched.+propSecretIDAEncodingDecoding bstr blist = ioProperty $ do+ frags <- SecretIDA.encode 5 30 Nothing bstr+ let chosen = fst $ unzip $ filter snd $ zip frags blist + if length chosen < 5 + then return True+ else + return $ bstr == SecretIDA.decode chosen+