Struct Bls12_381

pub struct Bls12_381;

Trait Implementations

impl IntrinsicCurve for Bls12_381

type Scalar = Bls12_381Scalar

type Point = Bls12_381G1Affine

fn msm(coeffs: &[Self::Scalar], bases: &[Self::Point]) -> Self::Point

Multi-scalar multiplication. The implementation may be specialized to use properties of the curve (e.g., if the curve order is prime).

impl LineMulMType<Bls12_381Fp2, SexticExtField<Bls12_381Fp2>> for Bls12_381

fn mul_023_by_023(l0: &EvaluatedLine<Fp2>, l1: &EvaluatedLine<Fp2>) -> [Fp2; 5]

Multiplies two lines in 023-form to get an element in 02345-form

fn mul_by_023(f: &Fp12, l: &EvaluatedLine<Fp2>) -> Fp12

Multiplies a line in 02345-form with a Fp12 element to get an Fp12 element

fn mul_by_02345(f: &Fp12, x: &[Fp2; 5]) -> Fp12

Multiplies a line in 02345-form with a Fp12 element to get an Fp12 element

impl MultiMillerLoop for Bls12_381

fn pre_loop( Q_acc: Vec<AffinePoint<Self::Fp2>>, Q: &[AffinePoint<Self::Fp2>], c: Option<Self::Fp12>, xy_fracs: &[(Self::Fp, Self::Fp)], ) -> (Self::Fp12, Vec<AffinePoint<Self::Fp2>>)

The expected output of this function when running the Miller loop with embedded exponent is c^3 * l_{3Q}

fn post_loop( f: &Self::Fp12, Q_acc: Vec<AffinePoint<Self::Fp2>>, _Q: &[AffinePoint<Self::Fp2>], _c: Option<Self::Fp12>, _xy_fracs: &[(Self::Fp, Self::Fp)], ) -> (Self::Fp12, Vec<AffinePoint<Self::Fp2>>)

After running the main body of the Miller loop, we conjugate f due to the curve seed x being negative.

const SEED_ABS: u64 = 15_132_376_222_941_642_752u64

const PSEUDO_BINARY_ENCODING: &[i8] = _

type Fp = Bls12_381Fp

type Fp12 = SexticExtField<Bls12_381Fp2>

fn evaluate_lines_vec( f: Self::Fp12, lines: Vec<EvaluatedLine<Self::Fp2>>, ) -> Self::Fp12

Function to evaluate the line functions of the Miller loop

fn multi_miller_loop( P: &[AffinePoint<Self::Fp>], Q: &[AffinePoint<Self::Fp2>], ) -> Self::Fp12

Runs the multi-Miller loop with no embedded exponent

fn multi_miller_loop_embedded_exp( P: &[AffinePoint<Self::Fp>], Q: &[AffinePoint<Self::Fp2>], c: Option<Self::Fp12>, ) -> Self::Fp12

Runs the multi-Miller loop with an embedded exponent, removing the need to calculate the residue witness in the final exponentiation step

impl PairingCheck for Bls12_381

type Fp = Bls12_381Fp

type Fp2 = Bls12_381Fp2

type Fp12 = SexticExtField<Bls12_381Fp2>

fn pairing_check_hint( P: &[AffinePoint<Self::Fp>], Q: &[AffinePoint<Self::Fp2>], ) -> (Self::Fp12, Self::Fp12)

Given points P[], Q[], computes the multi-Miller loop and then returns the final exponentiation hint from Novakovic-Eagon https://eprint.iacr.org/2024/640.pdf.

fn pairing_check( P: &[AffinePoint<Self::Fp>], Q: &[AffinePoint<Self::Fp2>], ) -> Result<(), PairingCheckError>

impl PairingIntrinsics for Bls12_381

const PAIRING_IDX: usize = 1usize

Index for custom intrinsic opcode determination.

const XI: Fp2 = _

The sextic extension Fp12 is Fp2[X] / (X^6 - \xi), where \xi is a non-residue.

const FROBENIUS_COEFFS: [[Self::Fp2; 5]; 12] = _

Multiplication constants for the Frobenius map for coefficients in Fp2 c1..=c5 for powers 0..12 FROBENIUS_COEFFS[i][j] = \xi^{(j + 1) * (p^i - 1)/6} when p = 1 (mod 6)

type Fp = Bls12_381Fp

type Fp2 = Bls12_381Fp2

type Fp12 = SexticExtField<Bls12_381Fp2>