Safe Haskell	None
Language	Haskell2010

Crypto.Spake2.Group

Description

Synopsis

Documentation

class Group group where Source #

A mathematical group intended to be used with SPAKE2.

Notes:

This is a much richer interface than one would expect from a group purely derived from abstract algebra
jml thinks this is relevant to all Diffie-Hellman cryptography, but too ignorant to say for sure
Is this group automatically abelian? cyclic? Must it have these properties?

Minimal complete definition

elementAdd, elementNegate, groupIdentity, scalarMultiply, integerToScalar, scalarToInteger, encodeElement, decodeElement, generateElement, elementSizeBits, scalarSizeBits, arbitraryElement

Associated Types

type Element group :: * Source #

An element of the group.

type Scalar group :: * Source #

A scalar for this group. Mathematically equivalent to an integer, but possibly stored differently for computational reasons.

Methods

elementAdd :: group -> Element group -> Element group -> Element group Source #

Group addition.

\x y z -> elementAdd group (elementAdd group x y) z == elementAdd group x (elementAdd group y z)

elementNegate :: group -> Element group -> Element group Source #

Inverse with respect to group addition.

\x -> (elementAdd group x (elementNegate group x)) == groupIdentity

\x -> (elementNegate group (elementNegate group x)) == x

elementSubtract :: group -> Element group -> Element group -> Element group Source #

Subtract one element from another.

\x y -> (elementSubtract group x y) == (elementAdd group x (elementNegate group y))

groupIdentity :: group -> Element group Source #

Identity of the group.

Note [Added for completeness]

\x -> (elementAdd group x groupIdentity) == x

\x -> (elementAdd group groupIdentity x) == x

scalarMultiply :: group -> Scalar group -> Element group -> Element group Source #

Multiply an element of the group with respect to a scalar.

This is equivalent to adding the element to itself N times, where N is a scalar.

integerToScalar :: group -> Integer -> Scalar group Source #

Get the scalar that corresponds to an integer.

Note [Added for completeness]

\x -> scalarToInteger group (integerToScalar group x) == x

scalarToInteger :: group -> Scalar group -> Integer Source #

Get the integer that corresponds to a scalar.

Note [Added for completeness]

\x -> integerToScalar group (scalarToInteger group x) == x

encodeElement :: ByteArray bytes => group -> Element group -> bytes Source #

Encode an element of the group into bytes.

Note [Byte encoding in Group]

\x -> decodeElement group (encodeElement group x) == CryptoPassed x

decodeElement :: ByteArray bytes => group -> bytes -> CryptoFailable (Element group) Source #

Decode an element into the group from some bytes.

Note [Byte encoding in Group]

generateElement :: MonadRandom randomly => group -> randomly (KeyPair group) Source #

Encode a scalar into bytes. | Generate a new random element of the group, with corresponding scalar.

elementSizeBits :: group -> Int Source #

Size of elements, in bits

scalarSizeBits :: group -> Int Source #

Size of scalars, in bits

arbitraryElement :: ByteArrayAccess bytes => group -> bytes -> Element group Source #

Deterministically create an arbitrary element from a seed bytestring.

XXX: jml would much rather this take a scalar, an element, or even an integer, rather than bytes because bytes mean that the group instances have to know about hash algorithms and HKDF. If the IntegerGroup class in SPAKE2 also oversized its input, then it and the ed25519 implementation would have identical decoding.

Instances

Group Ed25519 Source #
Associated Types type Element Ed25519 :: * Source # type Scalar Ed25519 :: * Source # Methods elementAdd :: Ed25519 -> Element Ed25519 -> Element Ed25519 -> Element Ed25519 Source # elementNegate :: Ed25519 -> Element Ed25519 -> Element Ed25519 Source # elementSubtract :: Ed25519 -> Element Ed25519 -> Element Ed25519 -> Element Ed25519 Source # groupIdentity :: Ed25519 -> Element Ed25519 Source # scalarMultiply :: Ed25519 -> Scalar Ed25519 -> Element Ed25519 -> Element Ed25519 Source # integerToScalar :: Ed25519 -> Integer -> Scalar Ed25519 Source # scalarToInteger :: Ed25519 -> Scalar Ed25519 -> Integer Source # encodeElement :: ByteArray bytes => Ed25519 -> Element Ed25519 -> bytes Source # decodeElement :: ByteArray bytes => Ed25519 -> bytes -> CryptoFailable (Element Ed25519) Source # generateElement :: MonadRandom randomly => Ed25519 -> randomly (KeyPair Ed25519) Source # elementSizeBits :: Ed25519 -> Int Source # scalarSizeBits :: Ed25519 -> Int Source # arbitraryElement :: ByteArrayAccess bytes => Ed25519 -> bytes -> Element Ed25519 Source #
Group IntegerAddition Source #
Associated Types type Element IntegerAddition :: * Source # type Scalar IntegerAddition :: * Source # Methods elementAdd :: IntegerAddition -> Element IntegerAddition -> Element IntegerAddition -> Element IntegerAddition Source # elementNegate :: IntegerAddition -> Element IntegerAddition -> Element IntegerAddition Source # elementSubtract :: IntegerAddition -> Element IntegerAddition -> Element IntegerAddition -> Element IntegerAddition Source # groupIdentity :: IntegerAddition -> Element IntegerAddition Source # scalarMultiply :: IntegerAddition -> Scalar IntegerAddition -> Element IntegerAddition -> Element IntegerAddition Source # integerToScalar :: IntegerAddition -> Integer -> Scalar IntegerAddition Source # scalarToInteger :: IntegerAddition -> Scalar IntegerAddition -> Integer Source # encodeElement :: ByteArray bytes => IntegerAddition -> Element IntegerAddition -> bytes Source # decodeElement :: ByteArray bytes => IntegerAddition -> bytes -> CryptoFailable (Element IntegerAddition) Source # generateElement :: MonadRandom randomly => IntegerAddition -> randomly (KeyPair IntegerAddition) Source # elementSizeBits :: IntegerAddition -> Int Source # scalarSizeBits :: IntegerAddition -> Int Source # arbitraryElement :: ByteArrayAccess bytes => IntegerAddition -> bytes -> Element IntegerAddition Source #
Group IntegerGroup Source #
Associated Types type Element IntegerGroup :: * Source # type Scalar IntegerGroup :: * Source # Methods elementAdd :: IntegerGroup -> Element IntegerGroup -> Element IntegerGroup -> Element IntegerGroup Source # elementNegate :: IntegerGroup -> Element IntegerGroup -> Element IntegerGroup Source # elementSubtract :: IntegerGroup -> Element IntegerGroup -> Element IntegerGroup -> Element IntegerGroup Source # groupIdentity :: IntegerGroup -> Element IntegerGroup Source # scalarMultiply :: IntegerGroup -> Scalar IntegerGroup -> Element IntegerGroup -> Element IntegerGroup Source # integerToScalar :: IntegerGroup -> Integer -> Scalar IntegerGroup Source # scalarToInteger :: IntegerGroup -> Scalar IntegerGroup -> Integer Source # encodeElement :: ByteArray bytes => IntegerGroup -> Element IntegerGroup -> bytes Source # decodeElement :: ByteArray bytes => IntegerGroup -> bytes -> CryptoFailable (Element IntegerGroup) Source # generateElement :: MonadRandom randomly => IntegerGroup -> randomly (KeyPair IntegerGroup) Source # elementSizeBits :: IntegerGroup -> Int Source # scalarSizeBits :: IntegerGroup -> Int Source # arbitraryElement :: ByteArrayAccess bytes => IntegerGroup -> bytes -> Element IntegerGroup Source #

decodeScalar :: (ByteArrayAccess bytes, Group group) => group -> bytes -> Scalar group Source #

Map some arbitrary bytes into a scalar in a group.

elementSizeBytes :: Group group => group -> Int Source #

Size of elements in a group, in bits.

scalarSizeBytes :: Group group => group -> Int Source #

Size of scalars in a group, in bytes.

data KeyPair group Source #

A group key pair composed of the private part (a scalar) and a public part (associated group element).

Constructors

KeyPair
Fields keyPairPublic :: !(Element group) keyPairPrivate :: !(Scalar group)