Trait CurveAffine

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pub trait CurveAffine:
    Copy
    + Clone
    + Sized
    + Send
    + Sync
    + Debug
    + Display
    + PartialEq
    + Eq
    + 'static {
    type Engine: Engine<Fr = Self::Scalar>;
    type Scalar: PrimeField + SqrtField;
    type Base: SqrtField;
    type Projective: CurveProjective<Affine = Self, Scalar = Self::Scalar>;
    type Prepared: Clone + Send + Sync + 'static;
    type Uncompressed: EncodedPoint<Affine = Self>;
    type Compressed: EncodedPoint<Affine = Self>;
    type Pair: CurveAffine<Pair = Self>;
    type PairingResult: Field;

Show 21 methods    // Required methods
    fn zero() -> Self;
    fn one() -> Self;
    fn is_zero(&self) -> bool;
    fn negate(&mut self);
    fn mul<S: Into<<Self::Scalar as PrimeField>::Repr>>(
        &self,
        other: S,
    ) -> Self::Projective;
    fn prepare(&self) -> Self::Prepared;
    fn pairing_with(&self, other: &Self::Pair) -> Self::PairingResult;
    fn into_projective(&self) -> Self::Projective;
    fn as_tuple(&self) -> (&Self::Base, &Self::Base);
    unsafe fn as_tuple_mut(&mut self) -> (&mut Self::Base, &mut Self::Base);
    fn sum_of_products(
        bases: &[Self],
        scalars: &[&[u64; 4]],
    ) -> Self::Projective;
    fn find_pippinger_window(num_components: usize) -> usize;
    fn find_pippinger_window_via_estimate(num_components: usize) -> usize;
    fn sum_of_products_pippinger(
        bases: &[Self],
        scalars: &[&[u64; 4]],
        window: usize,
    ) -> Self::Projective;
    fn sum_of_products_precomp_256(
        bases: &[Self],
        scalars: &[&[u64; 4]],
        pre: &[Self],
    ) -> Self::Projective;
    fn precomp_3(&self, pre: &mut [Self]);
    fn mul_precomp_3<S: Into<<Self::Scalar as PrimeField>::Repr>>(
        &self,
        other: S,
        pre: &[Self],
    ) -> Self::Projective;
    fn precomp_256(&self, pre: &mut [Self]);
    fn mul_precomp_256<S: Into<<Self::Scalar as PrimeField>::Repr>>(
        &self,
        other: S,
        pre: &[Self],
    ) -> Self::Projective;

    // Provided methods
    fn into_compressed(&self) -> Self::Compressed { ... }
    fn into_uncompressed(&self) -> Self::Uncompressed { ... }
}

Expand description

Affine representation of an elliptic curve point guaranteed to be in the correct prime order subgroup.

Required Associated Types§

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Required Methods§

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fn zero() -> Self

Returns the additive identity.

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fn one() -> Self

Returns a fixed generator of unknown exponent.

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fn is_zero(&self) -> bool

Determines if this point represents the point at infinity; the additive identity.

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fn negate(&mut self)

Negates this element.

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fn mul<S: Into<<Self::Scalar as PrimeField>::Repr>>( &self, other: S, ) -> Self::Projective

Performs scalar multiplication of this element with mixed addition.

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fn prepare(&self) -> Self::Prepared

Prepares this element for pairing purposes.

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fn pairing_with(&self, other: &Self::Pair) -> Self::PairingResult

Perform a pairing

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fn into_projective(&self) -> Self::Projective

Converts this element into its affine representation.

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fn as_tuple(&self) -> (&Self::Base, &Self::Base)

Borrow references to the X and Y coordinates of this point.

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unsafe fn as_tuple_mut(&mut self) -> (&mut Self::Base, &mut Self::Base)

Borrow mutable references to the X and Y coordinates of this point. Unsafe, because incorrectly modifying the coordinates violates the guarantee that the point must be on the curve and in the correct subgroup.

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fn sum_of_products(bases: &[Self], scalars: &[&[u64; 4]]) -> Self::Projective

given x, compute x^3+b multiplication of many points compute s1 * p1 + … + sn * pn simultaneously

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fn find_pippinger_window(num_components: usize) -> usize

Find the optimal window for running Pippinger’s algorithm; preprogrammed values

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fn find_pippinger_window_via_estimate(num_components: usize) -> usize

Find the optimal window for running Pippinger’s algorithm; computed values via an estimate of running time

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fn sum_of_products_pippinger( bases: &[Self], scalars: &[&[u64; 4]], window: usize, ) -> Self::Projective

multiplication of many points with Pippinger’s algorithm of window size w compute s1 * p1 + … + sn * pn simultaneously

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fn sum_of_products_precomp_256( bases: &[Self], scalars: &[&[u64; 4]], pre: &[Self], ) -> Self::Projective

multiplication of many points with precompuation compute s1 * p1 + … + sn * pn simultaneously assuming pre[j*256+i] = (\sum_{b such that bth bit of i is 1} 2^{32i}) * bases[j] for each j and i in 0..256

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