Safe Haskell	None
Language	Haskell2010

Protocol.Election

Contents

Type Encryption
- Type EncryptionNonce
Type Proof
Type Question
Type Answer
- Type ErrorAnswer
Type Election
- Type Hash
Type Ballot
- Type Signature
- Type ErrorBallot

Synopsis

data Encryption q = Encryption {
- encryption_nonce :: G q
- encryption_vault :: G q
}
type EncryptionNonce = E
encrypt :: Monad m => RandomGen r => SubGroup q => PublicKey q -> E q -> StateT r m (EncryptionNonce q, Encryption q)
data Proof q = Proof {
- proof_challenge :: Challenge q
- proof_response :: E q
}
type Challenge = E
type Oracle list q = list (Commitment q) -> Challenge q
prove :: Monad m => RandomGen r => SubGroup q => Functor list => E q -> list (Commitment q) -> Oracle list q -> StateT r m (Proof q)
type Commitment = G
commit :: SubGroup q => Proof q -> G q -> G q -> Commitment q
type Opinion = E
type Disjunction = G
booleanDisjunctions :: SubGroup q => [Disjunction q]
intervalDisjunctions :: SubGroup q => Opinion q -> Opinion q -> [Disjunction q]
newtype DisjProof q = DisjProof [Proof q]
proveEncryption :: forall m r q. Monad m => RandomGen r => SubGroup q => PublicKey q -> ZKP -> [Disjunction q] -> Opinion q -> (EncryptionNonce q, Encryption q) -> StateT r (ExceptT ErrorProove m) (DisjProof q)
verifyEncryption :: Monad m => SubGroup q => PublicKey q -> ZKP -> [Disjunction q] -> (Encryption q, DisjProof q) -> ExceptT ErrorValidateEncryption m Bool
encryptionStatement :: SubGroup q => ZKP -> Encryption q -> ByteString
encryptionCommitments :: SubGroup q => PublicKey q -> Encryption q -> (Disjunction q, Proof q) -> [G q]
newtype ZKP = ZKP ByteString
data ErrorProove = ErrorProove_InvalidOpinion Natural Natural
data ErrorValidateEncryption = ErrorValidateEncryption_InvalidProofLength Natural Natural
data Question q = Question {
- question_text :: Text
- question_choices :: [Text]
- question_mini :: Opinion q
- question_maxi :: Opinion q
}
data Answer q = Answer {
- answer_opinions :: [(Encryption q, DisjProof q)]
- answer_sumProof :: DisjProof q
}
data ErrorAnswer
- = ErrorAnswer_WrongNumberOfOpinions Natural Natural
- | ErrorAnswer_WrongSumOfOpinions Natural Natural Natural
encryptAnswer :: Monad m => RandomGen r => SubGroup q => PublicKey q -> ZKP -> Question q -> [Bool] -> StateT r (ExceptT ErrorAnswer m) (Answer q)
verifyAnswer :: SubGroup q => PublicKey q -> ZKP -> Question q -> Answer q -> Bool
data Election q = Election {
- election_name :: Text
- election_description :: Text
- election_publicKey :: PublicKey q
- election_questions :: [Question q]
- election_uuid :: UUID
- election_hash :: Hash
}
newtype Hash = Hash Text
data Ballot q = Ballot {
- ballot_answers :: [Answer q]
- ballot_signature :: Maybe (Signature q)
- ballot_election_uuid :: UUID
- ballot_election_hash :: Hash
}
encryptBallot :: Monad m => RandomGen r => SubGroup q => Election q -> Maybe (SecretKey q) -> [[Bool]] -> StateT r (ExceptT ErrorBallot m) (Ballot q)
verifyBallot :: SubGroup q => Election q -> Ballot q -> Bool
data Signature q = Signature {
- signature_publicKey :: PublicKey q
- signature_proof :: Proof q
}
signatureStatement :: Foldable f => SubGroup q => f (Answer q) -> [G q]
signatureCommitments :: SubGroup q => ZKP -> Commitment q -> ByteString
data ErrorBallot
- = ErrorBallot_WrongNumberOfAnswers Natural Natural
- | ErrorBallot_Answer ErrorAnswer

Type `Encryption`

data Encryption q Source #

ElGamal-like encryption. Its security relies on the Discrete Logarithm problem.

Because (groupGen ^encNonce ^secKey == groupGen ^secKey ^encNonce), knowing secKey, one can divide encryption_vault by (encryption_nonce ^secKey) to decipher (groupGen ^clear), then clear must be small to be decryptable, because it is encrypted as a power of groupGen to enable the additive homomorphism.

Constructors

Encryption
Fields encryption_nonce :: G q Public part of the random `encNonce`: `(groupGen ^encNonce)` encryption_vault :: G q Encrypted clear: `(pubKey ^r * groupGen ^clear)`

Instances

Eq (Encryption q) Source #
Instance details Defined in Protocol.Election Methods (==) :: Encryption q -> Encryption q -> Bool # (/=) :: Encryption q -> Encryption q -> Bool #
Show (Encryption q) Source #
Instance details Defined in Protocol.Election Methods showsPrec :: Int -> Encryption q -> ShowS # show :: Encryption q -> String # showList :: [Encryption q] -> ShowS #
SubGroup q => Additive (Encryption q) Source #	Additive homomorphism. Using the fact that: `groupGen ^x * groupGen ^y == groupGen ^(x+y)`.
Instance details Defined in Protocol.Election Methods zero :: Encryption q Source # (+) :: Encryption q -> Encryption q -> Encryption q Source # sum :: Foldable f => f (Encryption q) -> Encryption q Source #

Type `EncryptionNonce`

type EncryptionNonce = E Source #

encrypt :: Monad m => RandomGen r => SubGroup q => PublicKey q -> E q -> StateT r m (EncryptionNonce q, Encryption q) Source #

(encrypt pubKey clear) returns an ElGamal-like Encryption.

WARNING: the secret encryption nonce (encNonce) is returned alongside the Encryption in order to prove the validity of the encrypted clear in prove, but this secret encNonce MUST be forgotten after that, as it may be used to decipher the Encryption without the secret key associated with pubKey.

Type `Proof`

data Proof q Source #

Proof of knowledge of a discrete logarithm: secret == logBase base (base^secret).

NOTE: Since (pubKey == groupGen ^secKey), then: (logBase encryption_nonce (encryption_vault * encryption_nonce) == secKey + clear).

Constructors

Proof

Fields

proof_challenge :: Challenge q
Challenge sent by the verifier to the prover to ensure that the prover really has knowledge of the secret and is not replaying. Actually, proof_challenge is not sent in a prove, but derived from the prover's Commitments and statements with a collision resistant hash.
proof_response :: E q
Response sent by the prover to the verifier. Usually: nonce + sec * proof_challenge.
To be computed efficiently, it requires sec: either the secKey (in signature_proof) or the encNonce (in prove).

Instances

Eq (Proof q) Source #
Instance details Defined in Protocol.Election Methods (==) :: Proof q -> Proof q -> Bool # (/=) :: Proof q -> Proof q -> Bool #
Show (Proof q) Source #
Instance details Defined in Protocol.Election Methods showsPrec :: Int -> Proof q -> ShowS # show :: Proof q -> String # showList :: [Proof q] -> ShowS #

Type `Challenge`

type Challenge = E Source #

Type `Oracle`

type Oracle list q = list (Commitment q) -> Challenge q Source #

prove :: Monad m => RandomGen r => SubGroup q => Functor list => E q -> list (Commitment q) -> Oracle list q -> StateT r m (Proof q) Source #

(prove sec commitments oracle) returns a Proof that sec is known.

The Oracle is given the commitments raised to the power of the secret nonce of the Proof, as those are the commitments that the verifier will obtain when composing the proof_challenge and proof_response together (in encryptionCommitments).

NOTE: sec is secKey in signature_proof or encNonce in proveEncryption.

NOTE: The commitments are [groupGen] in signature_proof or [groupGen, pubKey] in proveEncryption.

WARNING: for prove to be a so-called strong Fiat-Shamir transformation (not a weak): the statement must be included in the hash (not only the commitments).

NOTE: a random nonce is used to ensure each prove does not reveal any information regarding the secret sec.

Type `Commitment`

type Commitment = G Source #

commit :: SubGroup q => Proof q -> G q -> G q -> Commitment q Source #

(commit proof x y) returns a Commitment from the given Proof with the knowledge of the verifier.

NOTE: Contrary to Helios-C specifications, (*) is used instead of (/) to avoid the performance cost of a modular exponentiation (^ (groupOrder - one)), this is compensated by using (-) instead of (+) in prove.

Type `Opinion`

type Opinion = E Source #

Index of a Disjunction within a list of them. It is encrypted as an Exponent by encrypt.

Type `Disjunction`

type Disjunction = G Source #

A Disjunction is an inversed (groupGen ^opinion) it's used in proveEncryption to generate a Proof that an encryption_vault contains a given (groupGen ^opinion),

booleanDisjunctions :: SubGroup q => [Disjunction q] Source #

intervalDisjunctions :: SubGroup q => Opinion q -> Opinion q -> [Disjunction q] Source #

Type `DisjProof`

newtype DisjProof q Source #

A list of Proofs to prove that the Opinion within an Encryption is indexing a Disjunction within a list of them, without knowing which Opinion it is.

Constructors

DisjProof [Proof q]

Instances

Eq (DisjProof q) Source #
Instance details Defined in Protocol.Election Methods (==) :: DisjProof q -> DisjProof q -> Bool # (/=) :: DisjProof q -> DisjProof q -> Bool #
Show (DisjProof q) Source #
Instance details Defined in Protocol.Election Methods showsPrec :: Int -> DisjProof q -> ShowS # show :: DisjProof q -> String # showList :: [DisjProof q] -> ShowS #

proveEncryption :: forall m r q. Monad m => RandomGen r => SubGroup q => PublicKey q -> ZKP -> [Disjunction q] -> Opinion q -> (EncryptionNonce q, Encryption q) -> StateT r (ExceptT ErrorProove m) (DisjProof q) Source #

(proveEncryption pubKey zkp disjs opin (encNonce, enc)) returns a DisjProof that enc encrypts one of the Disjunctions within disjs, without revealing which one it is.

A NIZK Disjunctive Chaum Pedersen Logarithm Equality is used.

verifyEncryption :: Monad m => SubGroup q => PublicKey q -> ZKP -> [Disjunction q] -> (Encryption q, DisjProof q) -> ExceptT ErrorValidateEncryption m Bool Source #

encryptionStatement :: SubGroup q => ZKP -> Encryption q -> ByteString Source #

encryptionCommitments :: SubGroup q => PublicKey q -> Encryption q -> (Disjunction q, Proof q) -> [G q] Source #

(encryptionCommitments pubKey enc (disj,proof)) returns the Commitments with only the knowledge of the verifier.

The Proof comes from prove of fakeProof in proveEncryption.

Type `ZKP`

newtype ZKP Source #

Zero-knowledge proof

Constructors

ZKP ByteString

Type `ErrorProove`

data ErrorProove Source #

Error raised by proveEncryption.

Constructors

ErrorProove_InvalidOpinion Natural Natural

When the opinion is not within the number of Disjunctions.

Instances

Eq ErrorProove Source #
Instance details Defined in Protocol.Election Methods (==) :: ErrorProove -> ErrorProove -> Bool # (/=) :: ErrorProove -> ErrorProove -> Bool #
Show ErrorProove Source #
Instance details Defined in Protocol.Election Methods showsPrec :: Int -> ErrorProove -> ShowS # show :: ErrorProove -> String # showList :: [ErrorProove] -> ShowS #

Type `ErrorValidateEncryption`

data ErrorValidateEncryption Source #

Error raised by verifyEncryption.

Constructors

ErrorValidateEncryption_InvalidProofLength Natural Natural

When the number of proofs is different than the number of Disjunctions.

Instances

Eq ErrorValidateEncryption Source #
Instance details Defined in Protocol.Election Methods (==) :: ErrorValidateEncryption -> ErrorValidateEncryption -> Bool # (/=) :: ErrorValidateEncryption -> ErrorValidateEncryption -> Bool #
Show ErrorValidateEncryption Source #
Instance details Defined in Protocol.Election Methods showsPrec :: Int -> ErrorValidateEncryption -> ShowS # show :: ErrorValidateEncryption -> String # showList :: [ErrorValidateEncryption] -> ShowS #

Type `Question`

data Question q Source #

Constructors

Question
Fields question_text :: Text question_choices :: [Text] question_mini :: Opinion q question_maxi :: Opinion q

Instances

Eq (Question q) Source #
Instance details Defined in Protocol.Election Methods (==) :: Question q -> Question q -> Bool # (/=) :: Question q -> Question q -> Bool #
Show (Question q) Source #
Instance details Defined in Protocol.Election Methods showsPrec :: Int -> Question q -> ShowS # show :: Question q -> String # showList :: [Question q] -> ShowS #

Type `Answer`

data Answer q Source #

Constructors

Answer
Fields answer_opinions :: [(Encryption q, DisjProof q)] Encrypted `Opinion` for each `question_choices` with a `DisjProof` that they belong to [0,1]. answer_sumProof :: DisjProof q Proofs that the sum of the `Opinon`s encrypted in `answer_opinions` is an element of `[mini..maxi]`. , answer_blankProof ::

Instances

Eq (Answer q) Source #
Instance details Defined in Protocol.Election Methods (==) :: Answer q -> Answer q -> Bool # (/=) :: Answer q -> Answer q -> Bool #
Show (Answer q) Source #
Instance details Defined in Protocol.Election Methods showsPrec :: Int -> Answer q -> ShowS # show :: Answer q -> String # showList :: [Answer q] -> ShowS #

Type `ErrorAnswer`

data ErrorAnswer Source #

Error raised by encryptAnswer.

Constructors

ErrorAnswer_WrongNumberOfOpinions Natural Natural	When the number of opinions is different than the number of choices (`question_choices`).
ErrorAnswer_WrongSumOfOpinions Natural Natural Natural	When the sum of opinions is not within the bounds of `question_mini` and `question_maxi`.

Instances

Eq ErrorAnswer Source #
Instance details Defined in Protocol.Election Methods (==) :: ErrorAnswer -> ErrorAnswer -> Bool # (/=) :: ErrorAnswer -> ErrorAnswer -> Bool #
Show ErrorAnswer Source #
Instance details Defined in Protocol.Election Methods showsPrec :: Int -> ErrorAnswer -> ShowS # show :: ErrorAnswer -> String # showList :: [ErrorAnswer] -> ShowS #

encryptAnswer :: Monad m => RandomGen r => SubGroup q => PublicKey q -> ZKP -> Question q -> [Bool] -> StateT r (ExceptT ErrorAnswer m) (Answer q) Source #

(encryptAnswer pubKey zkp quest opinions) returns an Answer validable by verifyAnswer, unless an ErrorAnswer is returned.

verifyAnswer :: SubGroup q => PublicKey q -> ZKP -> Question q -> Answer q -> Bool Source #

Type `Election`

data Election q Source #

Constructors

Election
Fields election_name :: Text election_description :: Text election_publicKey :: PublicKey q election_questions :: [Question q] election_uuid :: UUID election_hash :: Hash

Instances

Eq (Election q) Source #
Instance details Defined in Protocol.Election Methods (==) :: Election q -> Election q -> Bool # (/=) :: Election q -> Election q -> Bool #
Show (Election q) Source #
Instance details Defined in Protocol.Election Methods showsPrec :: Int -> Election q -> ShowS # show :: Election q -> String # showList :: [Election q] -> ShowS #

Type `Hash`

newtype Hash Source #

Constructors

Hash Text

Instances

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

Type `Ballot`

data Ballot q Source #

Constructors

Ballot
Fields ballot_answers :: [Answer q] ballot_signature :: Maybe (Signature q) ballot_election_uuid :: UUID ballot_election_hash :: Hash

encryptBallot :: Monad m => RandomGen r => SubGroup q => Election q -> Maybe (SecretKey q) -> [[Bool]] -> StateT r (ExceptT ErrorBallot m) (Ballot q) Source #

(encryptBallot elec (Just secKey) opinionsByQuest) returns a Ballot signed by secKey (the voter's secret key) where opinionsByQuest is a list of Opinions on each question_choices of each election_questions.

verifyBallot :: SubGroup q => Election q -> Ballot q -> Bool Source #

Type `Signature`

data Signature q Source #

Schnorr-like signature.

Used to avoid Ballot stuffing.

Constructors

Signature
Fields signature_publicKey :: PublicKey q signature_proof :: Proof q

signatureStatement :: Foldable f => SubGroup q => f (Answer q) -> [G q] Source #

(signatureStatement answers) returns all the encryption_nonces and encryption_vaults of the given answers.

signatureCommitments :: SubGroup q => ZKP -> Commitment q -> ByteString Source #

(signatureCommitments zkp commitment) returns the hashable content from the knowledge of the verifier.

Type `ErrorBallot`

data ErrorBallot Source #

Error raised by encryptBallot.

Constructors

ErrorBallot_WrongNumberOfAnswers Natural Natural	When the number of answers is different than the number of questions.
ErrorBallot_Answer ErrorAnswer	When `encryptAnswer` raised an `ErrorAnswer`.

Instances

Eq ErrorBallot Source #
Instance details Defined in Protocol.Election Methods (==) :: ErrorBallot -> ErrorBallot -> Bool # (/=) :: ErrorBallot -> ErrorBallot -> Bool #
Show ErrorBallot Source #
Instance details Defined in Protocol.Election Methods showsPrec :: Int -> ErrorBallot -> ShowS # show :: ErrorBallot -> String # showList :: [ErrorBallot] -> ShowS #