Crypto.Spake2.Groups

Each of these implements the Group typeclass.

Documentation

data Ed25519

Constructors

Ed25519

Instances

Eq Ed25519

Methods

(==) :: Ed25519 -> Ed25519 -> Bool

(/=) :: Ed25519 -> Ed25519 -> Bool

Show Ed25519

Methods

showsPrec :: Int -> Ed25519 -> ShowS

show :: Ed25519 -> String

showList :: [Ed25519] -> ShowS

AbelianGroup Ed25519

Associated Types

type Scalar Ed25519 :: *

Methods

scalarMultiply :: Ed25519 -> Scalar Ed25519 -> Element Ed25519 -> Element Ed25519

integerToScalar :: Ed25519 -> Integer -> Scalar Ed25519

scalarToInteger :: Ed25519 -> Scalar Ed25519 -> Integer

scalarSizeBits :: Ed25519 -> Int

generateElement :: MonadRandom randomly => Ed25519 -> randomly (KeyPair Ed25519)

Group Ed25519

Associated Types

type Element Ed25519 :: *

Methods

elementAdd :: Ed25519 -> Element Ed25519 -> Element Ed25519 -> Element Ed25519

elementNegate :: Ed25519 -> Element Ed25519 -> Element Ed25519

elementSubtract :: Ed25519 -> Element Ed25519 -> Element Ed25519 -> Element Ed25519

groupIdentity :: Ed25519 -> Element Ed25519

encodeElement :: ByteArray bytes => Ed25519 -> Element Ed25519 -> bytes

decodeElement :: ByteArray bytes => Ed25519 -> bytes -> CryptoFailable (Element Ed25519)

elementSizeBits :: Ed25519 -> Int

arbitraryElement :: ByteArrayAccess bytes => Ed25519 -> bytes -> Element Ed25519

type Scalar Ed25519

type Scalar Ed25519 = Integer

type Element Ed25519

type Element Ed25519

data IntegerGroup

A finite group of integers with respect to multiplication modulo the group order.

Construct with makeIntegerGroup.

Constructors

IntegerGroup

Fields

• order :: !Integer
• subgroupOrder :: !Integer
• generator :: !Integer

Instances

Eq IntegerGroup

Methods

(==) :: IntegerGroup -> IntegerGroup -> Bool

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

Show IntegerGroup

Methods

showsPrec :: Int -> IntegerGroup -> ShowS

show :: IntegerGroup -> String

showList :: [IntegerGroup] -> ShowS

AbelianGroup IntegerGroup

Associated Types

type Scalar IntegerGroup :: *

Methods

scalarMultiply :: IntegerGroup -> Scalar IntegerGroup -> Element IntegerGroup -> Element IntegerGroup

integerToScalar :: IntegerGroup -> Integer -> Scalar IntegerGroup

scalarToInteger :: IntegerGroup -> Scalar IntegerGroup -> Integer

scalarSizeBits :: IntegerGroup -> Int

generateElement :: MonadRandom randomly => IntegerGroup -> randomly (KeyPair IntegerGroup)

Group IntegerGroup

Associated Types

type Element IntegerGroup :: *

Methods

elementAdd :: IntegerGroup -> Element IntegerGroup -> Element IntegerGroup -> Element IntegerGroup

elementNegate :: IntegerGroup -> Element IntegerGroup -> Element IntegerGroup

elementSubtract :: IntegerGroup -> Element IntegerGroup -> Element IntegerGroup -> Element IntegerGroup

groupIdentity :: IntegerGroup -> Element IntegerGroup

encodeElement :: ByteArray bytes => IntegerGroup -> Element IntegerGroup -> bytes

decodeElement :: ByteArray bytes => IntegerGroup -> bytes -> CryptoFailable (Element IntegerGroup)

elementSizeBits :: IntegerGroup -> Int

arbitraryElement :: ByteArrayAccess bytes => IntegerGroup -> bytes -> Element IntegerGroup

type Scalar IntegerGroup

type Scalar IntegerGroup = Integer

type Element IntegerGroup

type Element IntegerGroup = Integer

makeIntegerGroup :: Integer -> Integer -> Integer -> Maybe IntegerGroup

Construct an IntegerGroup.

Will fail if generator is '1', since having the identity for a generator means the subgroup is the entire group.

TODO: Find other things to check for validity.

i1024 :: IntegerGroup

1024 bit integer group.

Originally from http://haofeng66.googlepages.com/JPAKEDemo.java, via python-spake2.