//! Traits used to abstract Ciphersuites.

use std::{
    fmt::Debug,
    ops::{Add, Mul, Sub},
};

use rand_core::{CryptoRng, RngCore};

use crate::{Error, FieldError, GroupError, Signature, VerifyingKey};

/// A prime order finite field GF(q) over which all scalar values for our prime order group can be
/// multiplied are defined.
///
/// This trait does not have to be implemented for a finite field scalar itself, it can be a
/// pass-through, implemented for a type just for the ciphersuite, and calls through to another
/// implementation underneath, so that this trait does not have to be implemented for types you
/// don't own.
pub trait Field: Copy + Clone {
    /// An element of the scalar field GF(p).
    /// The Eq/PartialEq implementation MUST be constant-time.
    type Scalar: Add<Output = Self::Scalar>
        + Copy
        + Clone
        + Eq
        + Mul<Output = Self::Scalar>
        + PartialEq
        + Sub<Output = Self::Scalar>;

    /// A unique byte array buf of fixed length N.
    type Serialization: AsRef<[u8]> + Debug + TryFrom<Vec<u8>>;

    /// Returns the zero element of the field, the additive identity.
    fn zero() -> Self::Scalar;

    /// Returns the one element of the field, the multiplicative identity.
    fn one() -> Self::Scalar;

    /// Computes the multiplicative inverse of an element of the scalar field, failing if the
    /// element is zero.
    fn invert(scalar: &Self::Scalar) -> Result<Self::Scalar, FieldError>;

    /// Generate a random scalar from the entire space [0, l-1]
    ///
    /// <https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-14.html#section-3.1-3.3>
    fn random<R: RngCore + CryptoRng>(rng: &mut R) -> Self::Scalar;

    /// A member function of a [`Field`] that maps a [`Scalar`] to a unique byte array buf of
    /// fixed length Ne.
    ///
    /// <https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-14.html#section-3.1-3.8>
    fn serialize(scalar: &Self::Scalar) -> Self::Serialization;

    /// A member function of a [`Field`] that maps a [`Scalar`] to a unique byte array buf of
    /// fixed length Ne, in little-endian order.
    ///
    /// This is used internally.
    fn little_endian_serialize(scalar: &Self::Scalar) -> Self::Serialization;

    /// A member function of a [`Field`] that attempts to map a byte array `buf` to a [`Scalar`].
    ///
    /// Fails if the input is not a valid byte representation of an [`Scalar`] of the
    /// [`Field`]. This function can raise an [`Error`] if deserialization fails.
    ///
    /// <https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-14.html#section-3.1-3.9>
    fn deserialize(buf: &Self::Serialization) -> Result<Self::Scalar, FieldError>;
}

/// An element of the [`Ciphersuite`] `C`'s [`Group`]'s scalar [`Field`].
pub type Scalar<C> = <<<C as Ciphersuite>::Group as Group>::Field as Field>::Scalar;

/// A prime-order group (or subgroup) that provides everything we need to create and verify Schnorr
/// signatures.
///
/// This trait does not have to be implemented for the curve/element/point itself, it can be a
/// pass-through, implemented for a type just for the ciphersuite, and calls through to another
/// implementation underneath, so that this trait does not have to be implemented for types you
/// don't own.
pub trait Group: Copy + Clone + PartialEq {
    /// A prime order finite field GF(q) over which all scalar values for our prime order group can
    /// be multiplied are defined.
    type Field: Field;

    /// An element of our group that we will be computing over.
    type Element: Add<Output = Self::Element>
        + Copy
        + Clone
        + Eq
        + Mul<<Self::Field as Field>::Scalar, Output = Self::Element>
        + PartialEq
        + Sub<Output = Self::Element>;

    /// A unique byte array buf of fixed length N.
    ///
    /// Little-endian!
    type Serialization: AsRef<[u8]> + Debug + TryFrom<Vec<u8>>;

    /// The order of the the quotient group when the prime order subgroup divides the order of the
    /// full curve group.
    ///
    /// If using a prime order elliptic curve, the cofactor should be 1 in the scalar field.
    fn cofactor() -> <Self::Field as Field>::Scalar;

    /// Additive [identity] of the prime order group.
    ///
    /// [identity]: https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-14.html#section-3.1-3.2
    fn identity() -> Self::Element;

    /// The fixed generator element of the prime order group.
    ///
    /// The 'base' of ['ScalarBaseMult()'] from the spec.
    ///
    /// [`ScalarBaseMult()`]: https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-14.html#section-3.1-3.5
    fn generator() -> Self::Element;

    /// A member function of a group _G_ that maps an [`Element`] to a unique byte array buf of
    /// fixed length Ne.
    ///
    /// <https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-14.html#section-3.1-3.6>
    fn serialize(element: &Self::Element) -> Self::Serialization;

    /// A member function of a [`Group`] that attempts to map a byte array `buf` to an [`Element`].
    ///
    /// Fails if the input is not a valid byte representation of an [`Element`] of the
    /// [`Group`]. This function can raise an [`Error`] if deserialization fails or if the
    /// resulting [`Element`] is the identity element of the group
    ///
    /// <https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-14.html#section-3.1-3.7>
    fn deserialize(buf: &Self::Serialization) -> Result<Self::Element, GroupError>;
}

/// An element of the [`Ciphersuite`] `C`'s [`Group`].
pub type Element<C> = <<C as Ciphersuite>::Group as Group>::Element;

/// A [FROST ciphersuite] specifies the underlying prime-order group details and cryptographic hash
/// function.
///
/// [FROST ciphersuite]: https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-14.html#name-ciphersuites
pub trait Ciphersuite: Copy + Clone + PartialEq + Debug {
    /// The ciphersuite ID string. It should be equal to the contextString in
    /// the spec. For new ciphersuites, this should be a string that identifies
    /// the ciphersuite; it's recommended to use a similar format to the
    /// ciphersuites in the FROST spec, e.g. "FROST-RISTRETTO255-SHA512-v1".
    const ID: &'static str;

    /// The prime order group (or subgroup) that this ciphersuite operates over.
    type Group: Group;

    /// A unique byte array of fixed length.
    type HashOutput: AsRef<[u8]>;

    /// A unique byte array of fixed length that is the `Group::ElementSerialization` +
    /// `Group::ScalarSerialization`
    type SignatureSerialization: AsRef<[u8]> + TryFrom<Vec<u8>>;

    /// [H1] for a FROST ciphersuite.
    ///
    /// Maps arbitrary inputs to `Self::Scalar` elements of the prime-order group scalar field.
    ///
    /// [H1]: https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-14.html#name-cryptographic-hash-function
    fn H1(m: &[u8]) -> <<Self::Group as Group>::Field as Field>::Scalar;

    /// [H2] for a FROST ciphersuite.
    ///
    /// Maps arbitrary inputs to `Self::Scalar` elements of the prime-order group scalar field.
    ///
    /// [H2]: https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-14.html#name-cryptographic-hash-function
    fn H2(m: &[u8]) -> <<Self::Group as Group>::Field as Field>::Scalar;

    /// [H3] for a FROST ciphersuite.
    ///
    /// Maps arbitrary inputs to `Self::Scalar` elements of the prime-order group scalar field.
    ///
    /// [H3]: https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-14.html#name-cryptographic-hash-function
    fn H3(m: &[u8]) -> <<Self::Group as Group>::Field as Field>::Scalar;

    /// [H4] for a FROST ciphersuite.
    ///
    /// Usually an an alias for the ciphersuite hash function _H_ with domain separation applied.
    ///
    /// [H4]: https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-14.html#name-cryptographic-hash-function
    fn H4(m: &[u8]) -> Self::HashOutput;

    /// [H5] for a FROST ciphersuite.
    ///
    /// Usually an an alias for the ciphersuite hash function _H_ with domain separation applied.
    ///
    /// [H5]: https://github.com/cfrg/draft-irtf-cfrg-frost/blob/master/draft-irtf-cfrg-frost.md#cryptographic-hash
    fn H5(m: &[u8]) -> Self::HashOutput;

    /// Hash function for a FROST ciphersuite, used for the DKG.
    ///
    /// The DKG it not part of the specification, thus this is optional.
    /// It can return None if DKG is not supported by the Ciphersuite. This is
    /// the default implementation.
    ///
    /// Maps arbitrary inputs to non-zero `Self::Scalar` elements of the prime-order group scalar field.
    fn HDKG(_m: &[u8]) -> Option<<<Self::Group as Group>::Field as Field>::Scalar> {
        None
    }

    /// Hash function for a FROST ciphersuite, used for deriving identifiers from strings.
    ///
    /// This feature is not part of the specification and is just a convenient
    /// way of creating identifiers. Therefore it can return None if this is not supported by the
    /// Ciphersuite. This is the default implementation.
    ///
    /// Maps arbitrary inputs to non-zero `Self::Scalar` elements of the prime-order group scalar field.
    fn HID(_m: &[u8]) -> Option<<<Self::Group as Group>::Field as Field>::Scalar> {
        None
    }

    /// Verify a signature for this ciphersuite. The default implementation uses the "cofactored"
    /// equation (it multiplies by the cofactor returned by [`Group::cofactor()`]).
    ///
    /// # Cryptographic Safety
    ///
    /// You may override this to provide a tailored implementation, but if the ciphersuite defines it,
    /// it must also multiply by the cofactor to comply with the RFC. Note that batch verification
    /// (see [`crate::batch::Verifier`]) also uses the default implementation regardless whether a
    /// tailored implementation was provided.
    fn verify_signature(
        msg: &[u8],
        signature: &Signature<Self>,
        public_key: &VerifyingKey<Self>,
    ) -> Result<(), Error<Self>> {
        let c = crate::challenge::<Self>(&signature.R, public_key, msg);

        public_key.verify_prehashed(c, signature)
    }
}