Safe Haskell	None
Language	Haskell2010

PrimeField

Synopsis

data P
unP :: P -> Integer
data Q
unQ :: Q -> Integer
data G
unG :: G -> Integer
data SPF
spfP :: SPF -> P
spfQ :: SPF -> Q
spfG :: SPF -> G
mkSPF :: MonadRandom m => Int -> m SPF
mkSPF' :: Integer -> Integer -> Integer -> Maybe SPF
type SPFM = ReaderT SPF
runSPFT :: SPF -> SPFM m a -> m a
runSPFM :: SPF -> SPFM Identity a -> a
gexpSafeSPF :: SPF -> Integer -> Integer
gexpSafeSPFM :: forall (m :: Type -> Type). Monad m => Integer -> SPFM m Integer
expSafeSPF :: SPF -> Integer -> Integer -> Integer
expSafeSPFM :: forall (m :: Type -> Type). Monad m => Integer -> Integer -> SPFM m Integer
randomInZq :: MonadRandom m => SPF -> m Integer
randomInZqM :: forall (m :: Type -> Type). MonadRandom m => SPFM m Integer
randomInZp :: MonadRandom m => SPF -> m Integer
randomInZpM :: forall (m :: Type -> Type). MonadRandom m => SPFM m Integer
modp :: SPF -> Integer -> Integer
modpM :: forall (m :: Type -> Type). Monad m => Integer -> SPFM m Integer
(|*|) :: forall (m :: Type -> Type). Monad m => SPFM m Integer -> SPFM m Integer -> SPFM m Integer
(|+|) :: forall (m :: Type -> Type). Monad m => SPFM m Integer -> SPFM m Integer -> SPFM m Integer

Documentation

data P Source #

A large, safe prime, p = 2q + 1, where q is a large prime

Instances

Instances details

Show P Source #
Instance details Defined in PrimeField Methods showsPrec :: Int -> P -> ShowS # show :: P -> String # showList :: [P] -> ShowS #
Eq P Source #
Instance details Defined in PrimeField Methods (==) :: P -> P -> Bool # (/=) :: P -> P -> Bool #
Ord P Source #
Instance details Defined in PrimeField Methods compare :: P -> P -> Ordering # (<) :: P -> P -> Bool # (<=) :: P -> P -> Bool # (>) :: P -> P -> Bool # (>=) :: P -> P -> Bool # max :: P -> P -> P # min :: P -> P -> P #

unP :: P -> Integer Source #

data Q Source #

A large prime such that p = 2q + 1 and p is also prime

Instances

Instances details

Show Q Source #
Instance details Defined in PrimeField Methods showsPrec :: Int -> Q -> ShowS # show :: Q -> String # showList :: [Q] -> ShowS #
Eq Q Source #
Instance details Defined in PrimeField Methods (==) :: Q -> Q -> Bool # (/=) :: Q -> Q -> Bool #
Ord Q Source #
Instance details Defined in PrimeField Methods compare :: Q -> Q -> Ordering # (<) :: Q -> Q -> Bool # (<=) :: Q -> Q -> Bool # (>) :: Q -> Q -> Bool # (>=) :: Q -> Q -> Bool # max :: Q -> Q -> Q # min :: Q -> Q -> Q #

unQ :: Q -> Integer Source #

data G Source #

A generator order Q for prime field order P

Instances

Instances details

Show G Source #
Instance details Defined in PrimeField Methods showsPrec :: Int -> G -> ShowS # show :: G -> String # showList :: [G] -> ShowS #
Eq G Source #
Instance details Defined in PrimeField Methods (==) :: G -> G -> Bool # (/=) :: G -> G -> Bool #
Ord G Source #
Instance details Defined in PrimeField Methods compare :: G -> G -> Ordering # (<) :: G -> G -> Bool # (<=) :: G -> G -> Bool # (>) :: G -> G -> Bool # (>=) :: G -> G -> Bool # max :: G -> G -> G # min :: G -> G -> G #

unG :: G -> Integer Source #

data SPF Source #

A Safe Prime Field (Zp): Q = large prime P = 2Q + 1, also prime G = generator for Zp order q

spfP :: SPF -> P Source #

spfQ :: SPF -> Q Source #

spfG :: SPF -> G Source #

mkSPF :: MonadRandom m => Int -> m SPF Source #

mkSPF' :: Integer -> Integer -> Integer -> Maybe SPF Source #

type SPFM = ReaderT SPF Source #

For computations using Safe Prime Field params

runSPFT :: SPF -> SPFM m a -> m a Source #

runSPFM :: SPF -> SPFM Identity a -> a Source #

gexpSafeSPF :: SPF -> Integer -> Integer Source #

Compute g^e mod p

gexpSafeSPFM :: forall (m :: Type -> Type). Monad m => Integer -> SPFM m Integer Source #

expSafeSPF :: SPF -> Integer -> Integer -> Integer Source #

Compute b^e mod p

expSafeSPFM :: forall (m :: Type -> Type). Monad m => Integer -> Integer -> SPFM m Integer Source #

randomInZq :: MonadRandom m => SPF -> m Integer Source #

Generate random number in Zq

randomInZqM :: forall (m :: Type -> Type). MonadRandom m => SPFM m Integer Source #

randomInZp :: MonadRandom m => SPF -> m Integer Source #

Generate random number in Zp

randomInZpM :: forall (m :: Type -> Type). MonadRandom m => SPFM m Integer Source #

modp :: SPF -> Integer -> Integer Source #

modpM :: forall (m :: Type -> Type). Monad m => Integer -> SPFM m Integer Source #

(|*|) :: forall (m :: Type -> Type). Monad m => SPFM m Integer -> SPFM m Integer -> SPFM m Integer Source #

(|+|) :: forall (m :: Type -> Type). Monad m => SPFM m Integer -> SPFM m Integer -> SPFM m Integer Source #