Migrate curve traits and tests, and WNAF, from pairing

src/lib.rs

@@ -0,0 +1,196 @@
+extern crate ff;
+extern crate rand;
+
+use ff::{PrimeField, PrimeFieldDecodingError, ScalarEngine, SqrtField};
+use std::error::Error;
+use std::fmt;
+
+pub mod tests;
+
+mod wnaf;
+pub use self::wnaf::Wnaf;
+
+/// Projective representation of an elliptic curve point guaranteed to be
+/// in the correct prime order subgroup.
+pub trait CurveProjective:
+    PartialEq
+    + Eq
+    + Sized
+    + Copy
+    + Clone
+    + Send
+    + Sync
+    + fmt::Debug
+    + fmt::Display
+    + rand::Rand
+    + 'static
+{
+    type Engine: ScalarEngine<Fr = Self::Scalar>;
+    type Scalar: PrimeField + SqrtField;
+    type Base: SqrtField;
+    type Affine: CurveAffine<Projective = Self, Scalar = Self::Scalar>;
+
+    /// Returns the additive identity.
+    fn zero() -> Self;
+
+    /// Returns a fixed generator of unknown exponent.
+    fn one() -> Self;
+
+    /// Determines if this point is the point at infinity.
+    fn is_zero(&self) -> bool;
+
+    /// Normalizes a slice of projective elements so that
+    /// conversion to affine is cheap.
+    fn batch_normalization(v: &mut [Self]);
+
+    /// Checks if the point is already "normalized" so that
+    /// cheap affine conversion is possible.
+    fn is_normalized(&self) -> bool;
+
+    /// Doubles this element.
+    fn double(&mut self);
+
+    /// Adds another element to this element.
+    fn add_assign(&mut self, other: &Self);
+
+    /// Subtracts another element from this element.
+    fn sub_assign(&mut self, other: &Self) {
+        let mut tmp = *other;
+        tmp.negate();
+        self.add_assign(&tmp);
+    }
+
+    /// Adds an affine element to this element.
+    fn add_assign_mixed(&mut self, other: &Self::Affine);
+
+    /// Negates this element.
+    fn negate(&mut self);
+
+    /// Performs scalar multiplication of this element.
+    fn mul_assign<S: Into<<Self::Scalar as PrimeField>::Repr>>(&mut self, other: S);
+
+    /// Converts this element into its affine representation.
+    fn into_affine(&self) -> Self::Affine;
+
+    /// Recommends a wNAF window table size given a scalar. Always returns a number
+    /// between 2 and 22, inclusive.
+    fn recommended_wnaf_for_scalar(scalar: <Self::Scalar as PrimeField>::Repr) -> usize;
+
+    /// Recommends a wNAF window size given the number of scalars you intend to multiply
+    /// a base by. Always returns a number between 2 and 22, inclusive.
+    fn recommended_wnaf_for_num_scalars(num_scalars: usize) -> usize;
+}
+
+/// Affine representation of an elliptic curve point guaranteed to be
+/// in the correct prime order subgroup.
+pub trait CurveAffine:
+    Copy + Clone + Sized + Send + Sync + fmt::Debug + fmt::Display + PartialEq + Eq + 'static
+{
+    type Engine: ScalarEngine<Fr = Self::Scalar>;
+    type Scalar: PrimeField + SqrtField;
+    type Base: SqrtField;
+    type Projective: CurveProjective<Affine = Self, Scalar = Self::Scalar>;
+    type Uncompressed: EncodedPoint<Affine = Self>;
+    type Compressed: EncodedPoint<Affine = Self>;
+
+    /// Returns the additive identity.
+    fn zero() -> Self;
+
+    /// Returns a fixed generator of unknown exponent.
+    fn one() -> Self;
+
+    /// Determines if this point represents the point at infinity; the
+    /// additive identity.
+    fn is_zero(&self) -> bool;
+
+    /// Negates this element.
+    fn negate(&mut self);
+
+    /// Performs scalar multiplication of this element with mixed addition.
+    fn mul<S: Into<<Self::Scalar as PrimeField>::Repr>>(&self, other: S) -> Self::Projective;
+
+    /// Converts this element into its affine representation.
+    fn into_projective(&self) -> Self::Projective;
+
+    /// Converts this element into its compressed encoding, so long as it's not
+    /// the point at infinity.
+    fn into_compressed(&self) -> Self::Compressed {
+        <Self::Compressed as EncodedPoint>::from_affine(*self)
+    }
+
+    /// Converts this element into its uncompressed encoding, so long as it's not
+    /// the point at infinity.
+    fn into_uncompressed(&self) -> Self::Uncompressed {
+        <Self::Uncompressed as EncodedPoint>::from_affine(*self)
+    }
+}
+
+/// An encoded elliptic curve point, which should essentially wrap a `[u8; N]`.
+pub trait EncodedPoint:
+    Sized + Send + Sync + AsRef<[u8]> + AsMut<[u8]> + Clone + Copy + 'static
+{
+    type Affine: CurveAffine;
+
+    /// Creates an empty representation.
+    fn empty() -> Self;
+
+    /// Returns the number of bytes consumed by this representation.
+    fn size() -> usize;
+
+    /// Converts an `EncodedPoint` into a `CurveAffine` element,
+    /// if the encoding represents a valid element.
+    fn into_affine(&self) -> Result<Self::Affine, GroupDecodingError>;
+
+    /// Converts an `EncodedPoint` into a `CurveAffine` element,
+    /// without guaranteeing that the encoding represents a valid
+    /// element. This is useful when the caller knows the encoding is
+    /// valid already.
+    ///
+    /// If the encoding is invalid, this can break API invariants,
+    /// so caution is strongly encouraged.
+    fn into_affine_unchecked(&self) -> Result<Self::Affine, GroupDecodingError>;
+
+    /// Creates an `EncodedPoint` from an affine point, as long as the
+    /// point is not the point at infinity.
+    fn from_affine(affine: Self::Affine) -> Self;
+}
+
+/// An error that may occur when trying to decode an `EncodedPoint`.
+#[derive(Debug)]
+pub enum GroupDecodingError {
+    /// The coordinate(s) do not lie on the curve.
+    NotOnCurve,
+    /// The element is not part of the r-order subgroup.
+    NotInSubgroup,
+    /// One of the coordinates could not be decoded
+    CoordinateDecodingError(&'static str, PrimeFieldDecodingError),
+    /// The compression mode of the encoded element was not as expected
+    UnexpectedCompressionMode,
+    /// The encoding contained bits that should not have been set
+    UnexpectedInformation,
+}
+
+impl Error for GroupDecodingError {
+    fn description(&self) -> &str {
+        match *self {
+            GroupDecodingError::NotOnCurve => "coordinate(s) do not lie on the curve",
+            GroupDecodingError::NotInSubgroup => "the element is not part of an r-order subgroup",
+            GroupDecodingError::CoordinateDecodingError(..) => "coordinate(s) could not be decoded",
+            GroupDecodingError::UnexpectedCompressionMode => {
+                "encoding has unexpected compression mode"
+            }
+            GroupDecodingError::UnexpectedInformation => "encoding has unexpected information",
+        }
+    }
+}
+
+impl fmt::Display for GroupDecodingError {
+    fn fmt(&self, f: &mut fmt::Formatter) -> Result<(), fmt::Error> {
+        match *self {
+            GroupDecodingError::CoordinateDecodingError(description, ref err) => {
+                write!(f, "{} decoding error: {}", description, err)
+            }
+            _ => write!(f, "{}", self.description()),
+        }
+    }
+}