Voting.Protocol.FFC

Finite Field Cryptography (FFC) is a method of implementing discrete logarithm cryptography using finite field mathematics.

Type FFC

data FFC

Mutiplicative subgroup of a Finite Prime Field.

NOTE: an FFC term-value is brought into the context of many functions through a type-variable c whose Reifies constraint enables to reflect that FFC at the term-level (a surprising technique but a very useful one). Doing like this is simpler than working in a Monad (like a Reader), and enables that FFC term to be used simply in instances' methods not supporting an inner Monad, like parseJSON, randomR, fromEnum or arbitrary. Aside from that, the sharing of FFC amongst several types is encoded at the type-level by including c as a phantom type of F, G and E.

Constructors

FFC

Fields

• ffc_name :: !Text
• ffc_fieldCharac :: !Natural

  The prime number characteristic of a Finite Prime Field.

  ElGamal's hardness to decrypt requires a large prime number to form the multiplicative subgroup.

• ffc_groupGen :: !Natural

  A generator of the multiplicative subgroup of the Finite Prime Field.

  NOTE: since ffc_fieldCharac is prime, the multiplicative subgroup is cyclic, and there are phi(fieldCharac-1) many choices for the generator of the group, where phi is the Euler totient function.

• ffc_groupOrder :: !Natural

  The order of the subgroup.

  WARNING: ffc_groupOrder MUST be a prime number dividing (ffc_fieldCharac-1) to ensure that ElGamal is secure in terms of the DDH assumption.

Instances

Eq FFC

Defined in Voting.Protocol.FFC

Methods

(==) :: FFC -> FFC -> Bool

(/=) :: FFC -> FFC -> Bool

Show FFC

Defined in Voting.Protocol.FFC

Methods

showsPrec :: Int -> FFC -> ShowS

show :: FFC -> String

showList :: [FFC] -> ShowS

Generic FFC

Defined in Voting.Protocol.FFC

Associated Types

type Rep FFC :: Type -> Type

Methods

from :: FFC -> Rep FFC x

to :: Rep FFC x -> FFC

ToJSON FFC

Defined in Voting.Protocol.FFC

Methods

toJSON :: FFC -> Value

toEncoding :: FFC -> Encoding

toJSONList :: [FFC] -> Value

toEncodingList :: [FFC] -> Encoding

FromJSON FFC

Defined in Voting.Protocol.FFC

Methods

parseJSON :: Value -> Parser FFC

parseJSONList :: Value -> Parser [FFC]

NFData FFC

Defined in Voting.Protocol.FFC

Methods

rnf :: FFC -> ()

ReifyCrypto FFC

Defined in Voting.Protocol.FFC

Methods

reifyCrypto :: FFC -> (forall c. (Reifies c FFC, CryptoParams FFC c) => Proxy c -> r) -> r

Key FFC

Defined in Voting.Protocol.FFC

Methods

cryptoType :: FFC -> Text

cryptoName :: FFC -> Text

randomSecretKey :: forall c (m :: Type -> Type) r. (Reifies c FFC, Monad m, RandomGen r) => StateT r m (SecretKey FFC c)

credentialSecretKey :: Reifies c FFC => UUID -> Credential -> SecretKey FFC c

publicKey :: Reifies c FFC => SecretKey FFC c -> PublicKey FFC c

Reifies c FFC => CryptoParams FFC c

Defined in Voting.Protocol.FFC

Methods

groupGen :: G FFC c

groupOrder :: Proxy c -> Natural

groupGenPowers :: [G FFC c]

groupGenInverses :: [G FFC c]

Eq (G FFC c)

Defined in Voting.Protocol.FFC

Methods

(==) :: G FFC c -> G FFC c -> Bool

(/=) :: G FFC c -> G FFC c -> Bool

Ord (G FFC c)

Defined in Voting.Protocol.FFC

Methods

compare :: G FFC c -> G FFC c -> Ordering

(<) :: G FFC c -> G FFC c -> Bool

(<=) :: G FFC c -> G FFC c -> Bool

(>) :: G FFC c -> G FFC c -> Bool

(>=) :: G FFC c -> G FFC c -> Bool

max :: G FFC c -> G FFC c -> G FFC c

min :: G FFC c -> G FFC c -> G FFC c

Show (G FFC c)

Defined in Voting.Protocol.FFC

Methods

showsPrec :: Int -> G FFC c -> ShowS

show :: G FFC c -> String

showList :: [G FFC c] -> ShowS

ToJSON (G FFC c)

Defined in Voting.Protocol.FFC

Methods

toJSON :: G FFC c -> Value

toEncoding :: G FFC c -> Encoding

toJSONList :: [G FFC c] -> Value

toEncodingList :: [G FFC c] -> Encoding

Reifies c FFC => FromJSON (G FFC c)

Defined in Voting.Protocol.FFC

Methods

parseJSON :: Value -> Parser (G FFC c)

parseJSONList :: Value -> Parser [G FFC c]

NFData (G FFC c)

Defined in Voting.Protocol.FFC

Methods

rnf :: G FFC c -> ()

Reifies c FFC => Random (G FFC c)

Defined in Voting.Protocol.FFC

Methods

randomR :: RandomGen g => (G FFC c, G FFC c) -> g -> (G FFC c, g)

random :: RandomGen g => g -> (G FFC c, g)

randomRs :: RandomGen g => (G FFC c, G FFC c) -> g -> [G FFC c]

randoms :: RandomGen g => g -> [G FFC c]

ToNatural (G FFC c)

Defined in Voting.Protocol.FFC

Methods

nat :: G FFC c -> Natural

Reifies c FFC => FromNatural (G FFC c)

Defined in Voting.Protocol.FFC

Methods

fromNatural :: Natural -> G FFC c

Reifies c FFC => EuclideanRing (G FFC c)

Defined in Voting.Protocol.FFC

Methods

inverse :: G FFC c -> G FFC c

(/) :: G FFC c -> G FFC c -> G FFC c

Reifies c FFC => Ring (G FFC c)

Defined in Voting.Protocol.FFC

Methods

negate :: G FFC c -> G FFC c

(-) :: G FFC c -> G FFC c -> G FFC c

Reifies c FFC => Semiring (G FFC c)

Defined in Voting.Protocol.FFC

Methods

one :: G FFC c

(*) :: G FFC c -> G FFC c -> G FFC c

Reifies c FFC => Additive (G FFC c)

Defined in Voting.Protocol.FFC

Methods

zero :: G FFC c

(+) :: G FFC c -> G FFC c -> G FFC c

sum :: Foldable f => f (G FFC c) -> G FFC c

type Rep FFC

Defined in Voting.Protocol.FFC

type Rep FFC = D1 ('MetaData "FFC" "Voting.Protocol.FFC" "majurity-protocol-0.0.10.20191104-inplace" 'False) (C1 ('MetaCons "FFC" 'PrefixI 'True) ((S1 ('MetaSel ('Just "ffc_name") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Text) :*: S1 ('MetaSel ('Just "ffc_fieldCharac") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Natural)) :*: (S1 ('MetaSel ('Just "ffc_groupGen") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Natural) :*: S1 ('MetaSel ('Just "ffc_groupOrder") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Natural))))

type FieldElement FFC

The type of the elements of a Finite Prime Field.

A field must satisfy the following properties:

• (f, (+), zero) forms an abelian group, called the additive group of f.
• (NonNull f, (*), one) forms an abelian group, called the multiplicative group of f.
• (*) is associative: (a*b)*c == a*(b*c) and a*(b*c) == (a*b)*c.
• (*) and (+) are both commutative: a*b == b*a and a+b == b+a
• (*) and (+) are both left and right distributive: a*(b+c) == (a*b) + (a*c) and (a+b)*c == (a*c) + (b*c)

The Natural is always within [0..fieldCharac-1].

Defined in Voting.Protocol.FFC

type FieldElement FFC = Natural

fieldCharac :: forall c. Reifies c FFC => Natural

Examples

weakFFC :: FFC

Weak parameters for debugging purposes only.

beleniosFFC :: FFC

Parameters used in Belenios. A 2048-bit fieldCharac of a Finite Prime Field, with a 256-bit groupOrder for a multiplicative subgroup generated by groupGen.