-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Multiparty Computation in Haskell
--   
--   hMPC is a Haskell package for secure multiparty computation (MPC).
--   
--   hMPC provides a runtime for performing computations on secret-shared
--   values, where parties interact by exchanging messages via peer-to-peer
--   connections. The hMPC protocols are based on Shamir's threshold secret
--   sharing scheme and withstand passive adversaries controlling less than
--   half of the parties.
--   
--   Secure integer arithmetic is supported for parameterized number
--   ranges, including support for comparison operations. Secure finite
--   field arithmetic is supported.
--   
--   The above operations are all available via Haskell's operator
--   overloading.
--   
--   Secure drop-in replacements for lots of Haskell built-in functions,
--   such as <a>all</a>, <a>sum</a>, <a>min</a>, <a>max</a> are provided,
--   mimicking the Haskell APIs as much as possible. Further operations for
--   container datatypes holding secret-shared data items are provided as
--   well (e.g., matrix-vector operations like secure dot products).
@package hMPC
@version 0.1.0.2


-- | This module collects all hGMP functions used by hMPC.
module Hgmp

-- | Return True if x is probably prime, else False if x is definitely
--   composite
isPrime :: Integer -> Bool

-- | Return the greatest probable prime number &lt; x, if any.
prevPrime :: Integer -> Integer

-- | Return y such that <tt>x*y == 1 modulo m</tt>.
invert :: Integer -> Integer -> Integer


-- | This module supports finite (Galois) fields.
--   
--   Function <a>gf</a> creates types implementing finite fields.
module FinFields

-- | Instantiate an object from a field and subsequently apply overloaded
--   operators such as <tt>(<a>+</a>)</tt>, <tt>(<a>-</a>)</tt>,
--   <tt>(<a>*</a>)</tt>, <tt>(<a>/</a>)</tt> etc., to compute with field
--   elements.
data FiniteField
FiniteField :: FiniteFieldMeta -> Integer -> FiniteField
[meta] :: FiniteField -> FiniteFieldMeta
[value] :: FiniteField -> Integer
Literal :: Integer -> FiniteField
[value] :: FiniteField -> Integer
data FiniteFieldMeta
FiniteFieldMeta :: Integer -> Int -> FiniteFieldMeta
[modulus] :: FiniteFieldMeta -> Integer
[byteLength] :: FiniteFieldMeta -> Int

-- | Create a finite (Galois) field for given modulus (prime number).
gf :: Integer -> FiniteField

-- | Return byte string representing the given list/ndarray of integers x.
toBytes :: Int -> [Integer] -> ByteString

-- | Return the list of integers represented by the given byte string.
fromBytes :: Int -> ByteString -> [Integer]
instance GHC.Show.Show FinFields.FiniteFieldMeta
instance GHC.Show.Show FinFields.FiniteField
instance GHC.Real.Fractional FinFields.FiniteField
instance GHC.Classes.Eq FinFields.FiniteField
instance GHC.Num.Num FinFields.FiniteField

module Parser

-- | Return parser results for command line arguments passed to the hMPC
--   runtime.
getArgParser :: IO Options

-- | Return parser for command line arguments passed to the hMPC runtime.
getArgParserExtra :: Parser a -> IO (Options, a)
data Options
Options :: [String] -> Integer -> Integer -> Integer -> Integer -> Int -> Bool -> Maybe Int -> Options
[parsParties] :: Options -> [String]
[m] :: Options -> Integer
[myPid] :: Options -> Integer
[threshold] :: Options -> Integer
[basePort] :: Options -> Integer
[secParam] :: Options -> Int
[noAsync] :: Options -> Bool
[nrThreads] :: Options -> Maybe Int


-- | Module for information-theoretic threshold secret sharing.
--   
--   Threshold secret sharing assumes secure channels for communication.
module Shamir

-- | Split each secret given in s into m random Shamir shares.
--   
--   The (maximum) degree for the Shamir polynomials is t, <tt>0 &lt;= t
--   &lt; m</tt>. Return matrix of shares, one row per party.
randomSplit :: RandomGen g => FiniteField -> [FiniteField] -> Integer -> Integer -> g -> ([[Integer]], g)

-- | Compute and store a recombination vector.
--   
--   A recombination vector depends on the field, the x-coordinates xs of
--   the shares and the x-coordinate x_r of the recombination point.
_recombinationVector :: FiniteField -> [Integer] -> Integer -> [Integer]

-- | Recombine shares given by points into secrets.
--   
--   Recombination is done for x-coordinates x_rs.
recombine :: FiniteField -> [IdSharesPair] -> [FiniteField]

-- | Couples a ID pi to the share list si.
type IdSharesPair = (Integer, [Integer])

module Types
type Dict = Map Int (MVar ByteString)
data Party
Party :: Integer -> String -> Integer -> Chan ByteString -> Maybe Socket -> MVar Dict -> MVar Int -> Party
[pid] :: Party -> Integer
[host] :: Party -> String
[port] :: Party -> Integer
[outChan] :: Party -> Chan ByteString
[sock] :: Party -> Maybe Socket
[dict] :: Party -> MVar Dict
[nbytesSent] :: Party -> MVar Int
data Barrier
Barrier :: MVar Int -> MVar () -> Barrier
[count] :: Barrier -> MVar Int
[signal] :: Barrier -> MVar ()
data Env
Env :: [Party] -> Int -> Options -> Barrier -> StdGen -> UTCTime -> Env
[parties] :: Env -> [Party]
[pc] :: Env -> Int
[options] :: Env -> Options
[forkIOBarrier] :: Env -> Barrier
[gen] :: Env -> StdGen
[startTime] :: Env -> UTCTime
type SIO a = StateT Env IO a
runSIO :: SIO a -> Env -> IO a
logging :: Priority -> String -> IO ()


-- | This module collects basic secure (secret-shared) types for hMPC.
--   
--   Secure number types all use common base classes, which ensures that
--   operators such as +,* are defined by operator overloading.
module SecTypes

-- | A secret-shared object.
--   
--   An MPC protocol operates on secret-shared objects of type
--   SecureObject. The basic Haskell operators are overloaded instances by
--   SecureTypes classes. An expression like a * b will create a new
--   SecureObject, which will eventually contain the product of a and b.
--   The product is computed asynchronously, using an instance of a
--   specific cryptographic protocol.
data SecureTypes

-- | Base class for secure (secret-shared) numbers.
SecFld :: FiniteField -> MVar FiniteField -> Int -> SecureTypes
[field] :: SecureTypes -> FiniteField
[share] :: SecureTypes -> MVar FiniteField
[bitLength] :: SecureTypes -> Int

-- | Base class for secure (secret-shared) finite field elements.
SecInt :: FiniteField -> MVar FiniteField -> Int -> SecureTypes
[field] :: SecureTypes -> FiniteField
[share] :: SecureTypes -> MVar FiniteField
[bitLength] :: SecureTypes -> Int
Literal :: MVar FiniteField -> SecureTypes
[share] :: SecureTypes -> MVar FiniteField

-- | Secure l-bit integers (<a>SecInt</a>).
secIntGen :: Int -> SIO (Integer -> SIO SecureTypes)

-- | Secure finite field (<a>SecFld</a>) of order q = p where p is a prime
--   number
secFldGen :: Integer -> Integer -> SIO SecureTypes
setShare :: SecureTypes -> Integer -> SIO SecureTypes


-- | This module provides basic support for asynchronous communication and
--   computation of secret-shared values.
module Asyncoro

-- | Open connections with other parties, if any.
createConnections :: Int -> [Party] -> IO [Party]

-- | Send payload labeled with pc to the peer.
--   
--   Message format consists of three parts:
--   
--   <ol>
--   <li>pc (8 bytes signed int)</li>
--   <li>payload_size (4 bytes unsigned int)</li>
--   <li>payload (byte string of length payload_size).</li>
--   </ol>
send :: Int -> ByteString -> Party -> SIO ()

-- | Receive payload labeled with given pc from the peer.
receive :: Int -> Party -> SIO (MVar ByteString)

-- | Transform <a>SecureTypes</a> into <a>FiniteField</a> by reading the
--   future <a>MVar</a> share that contains a <a>FiniteField</a>
--   (blocking).
class Gather a where {
    type Result a :: *;
}
gather :: Gather a => a -> SIO (Result a)

-- | <a>forkIO</a> the action monad asynchronously and return future
--   <a>MVar</a>. Provide the given state monad with its own program
--   counter space.
async :: SIO a -> SIO (MVar a)
asyncList :: Int -> SIO [a] -> SIO [MVar a]
asyncListList :: Int -> Int -> SIO [[a]] -> SIO [[MVar a]]

-- | Read the value from the future MVar (blocking).
await :: MVar a -> SIO a

-- | increment program counter in state.
incPC :: SIO Int
decreaseBarrier :: Barrier -> IO ()
instance Asyncoro.Gather SecTypes.SecureTypes
instance Asyncoro.Gather a => Asyncoro.Gather [a]
instance (Asyncoro.Gather a, Asyncoro.Gather b) => Asyncoro.Gather (a, b)
instance (Asyncoro.Gather a, Asyncoro.Gather b, Asyncoro.Gather c) => Asyncoro.Gather (a, b, c)


-- | The hMPC runtime module is used to execute secure multiparty
--   computations.
--   
--   Parties perform computations on secret-shared values by exchanging
--   messages. Shamir's threshold secret sharing scheme is used for finite
--   fields of any order exceeding the number of parties. hMPC provides
--   many secure data types, ranging from numeric types to more advanced
--   types, for which the corresponding operations are made available
--   through Haskell's mechanism for operator overloading.
module Runtime

-- | Secure l-bit integers (<a>SecInt</a>).
secIntGen :: Int -> SIO (Integer -> SIO SecureTypes)

-- | Secure finite field (<a>SecFld</a>) of order q = p where p is a prime
--   number
secFldGen :: Integer -> Integer -> SIO SecureTypes

-- | Runs <tt>MPC</tt> computation
runMpc :: SIO a -> IO a

-- | Runs <tt>MPC</tt> computation with user arguments
runMpcWithArgs :: Parser b -> (b -> SIO a) -> IO a

-- | Start and Stop hMPC runtime
runSession :: SIO a -> SIO a

-- | Input x to the computation.
--   
--   Value x is a secure object, or a list of secure objects.
class Input a b | a -> b
input :: Input a b => a -> SIO b

-- | Output the value of x to the receivers specified. Value x is a secure
--   object, or a list of secure objects.
--   
--   A secure integer is output as a Haskell Integer
class Output a b | a -> b
output :: Output a b => a -> SIO (MVar b)

-- | Transfer serializable Haskell objects
transfer :: Serialize a => a -> SIO (MVar [a])

-- | Secure addition of a and b.
(.+) :: SIO SecureTypes -> SIO SecureTypes -> SIO SecureTypes

-- | Secure subtraction of a and b.
(.-) :: SIO SecureTypes -> SIO SecureTypes -> SIO SecureTypes

-- | Secure multiplication of a and b.
(.*) :: SIO SecureTypes -> SIO SecureTypes -> SIO SecureTypes

-- | Secure division of a by b, for nonzero b.
(./) :: SIO SecureTypes -> SIO SecureTypes -> SIO SecureTypes

-- | Secure reciprocal (multiplicative field inverse) of a, for nonzero a.
srecip :: SIO SecureTypes -> SIO SecureTypes

-- | Secure exponentiation a raised to the power of b, for public integer
--   b.
(.^) :: SIO SecureTypes -> Integer -> SIO SecureTypes

-- | Secure comparison a &lt; b.
(.<) :: SIO SecureTypes -> SIO SecureTypes -> SIO SecureTypes

-- | Secure comparison a &lt;= b.
(.<=) :: SIO SecureTypes -> SIO SecureTypes -> SIO SecureTypes

-- | Secure comparison a &gt; b.
(.>) :: SIO SecureTypes -> SIO SecureTypes -> SIO SecureTypes

-- | Secure comparison a == b.
(.==) :: SIO SecureTypes -> SIO SecureTypes -> SIO SecureTypes

-- | Secure zero test a == 0.
isZero :: SIO SecureTypes -> SIO SecureTypes

-- | Secure public zero test of a.
isZeroPublic :: SIO SecureTypes -> SIO (MVar Bool)

-- | Secure sign(um) of a, return -1 if a &lt; 0 else 0 if a == 0 else 1.
--   
--   If Boolean flag LT is set, perform a secure less than zero test
--   instead, and return 1 if a &lt; 0 else 0, saving the work for a secure
--   equality test. If Boolean flag EQ is set, perform a secure equal to
--   zero test instead, and return 1 if a == 0 else 0, saving the work for
--   a secure comparison.
ssignum :: Bool -> Bool -> SIO SecureTypes -> SIO SecureTypes
argmaxfunc :: [[SIO SecureTypes]] -> ([SIO SecureTypes] -> [SIO SecureTypes] -> SIO SecureTypes) -> SIO (SIO SecureTypes, [SIO SecureTypes])

-- | Secure argmax of all given elements in x.
--   
--   In case of multiple occurrences of the maximum values, the index of
--   the first occurrence is returned.
argmax :: [SIO SecureTypes] -> SIO (SIO SecureTypes, SIO SecureTypes)

-- | Secure maximum of all given elements in x, similar to Haskell's
--   built-in maximum.
smaximum :: [SIO SecureTypes] -> SIO SecureTypes

-- | Secure sum of all elements in x, similar to Haskell's built-in sum.
ssum :: [SIO SecureTypes] -> SIO SecureTypes

-- | Secure product of all elements in x, similar to Haskell's product.
--   
--   Runs in log_2 len(x) rounds).
sproduct :: [SIO SecureTypes] -> SIO SecureTypes

-- | Secure all of elements in x, similar to Haskell's built-in all.
--   
--   Elements of x are assumed to be either 0 or 1 (Boolean). Runs in log_2
--   len(x) rounds).
sall :: [SIO SecureTypes] -> SIO SecureTypes

-- | Return n secure uniformly random bits of the given type.
randomBits :: SIO SecureTypes -> Int -> Bool -> SIO [SIO SecureTypes]

-- | Secure dot product of x and y (one resharing).
inProd :: [SIO SecureTypes] -> [SIO SecureTypes] -> SIO SecureTypes

-- | Secure entrywise multiplication of vectors x and y.
schurProd :: [SIO SecureTypes] -> [SIO SecureTypes] -> SIO [SIO SecureTypes]

-- | Secure matrix product of A with (transposed) B.
matrixProd :: [[SIO SecureTypes]] -> [[SIO SecureTypes]] -> Bool -> SIO [[SIO SecureTypes]]

-- | Secure selection between x and y based on condition c.
class IfElse a b | a -> b
ifElse :: IfElse a b => SIO SecureTypes -> a -> a -> SIO b
ifElseList :: SIO SecureTypes -> [SIO SecureTypes] -> [SIO SecureTypes] -> SIO [SIO SecureTypes]

-- | <a>forkIO</a> the action monad asynchronously and return future
--   <a>MVar</a>. Provide the given state monad with its own program
--   counter space.
async :: SIO a -> SIO (MVar a)

-- | Read the value from the future MVar (blocking).
await :: MVar a -> SIO a
instance Runtime.IfElse (Types.SIO SecTypes.SecureTypes) SecTypes.SecureTypes
instance Runtime.IfElse [Types.SIO SecTypes.SecureTypes] [Types.SIO SecTypes.SecureTypes]
instance Runtime.Output (Types.SIO SecTypes.SecureTypes) GHC.Num.Integer.Integer
instance Runtime.Output [Types.SIO SecTypes.SecureTypes] [GHC.Num.Integer.Integer]
instance Runtime.Reshare FinFields.FiniteField FinFields.FiniteField
instance Runtime.Reshare [FinFields.FiniteField] [FinFields.FiniteField]
instance Runtime.Input (Types.SIO SecTypes.SecureTypes) [Types.SIO SecTypes.SecureTypes]
instance Runtime.Input [Types.SIO SecTypes.SecureTypes] [[Types.SIO SecTypes.SecureTypes]]
instance GHC.Num.Num (Types.SIO SecTypes.SecureTypes)
instance GHC.Real.Fractional (Types.SIO SecTypes.SecureTypes)