Struct Bn254

pub struct Bn254;

Trait Implementations

impl FinalExp for Bn254

type Fp = Fq

type Fp2 = Fq2

type Fp12 = Fq12

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

Assert in circuit that the final exponentiation is equal to one. The actual final exponentiaton is calculated out of circuit via final_exp_hint. Scalar coefficients to the curve points must equal to zero, which is checked in a debug_assert.

fn final_exp_hint(f: &Self::Fp12) -> (Self::Fp12, Self::Fp12)

Generates a hint for the final exponentiation to be calculated out of circuit Input is the result of the Miller loop Output is c (residue witness inverse) and u (cubic nonresidue power)

impl LineMulDType<Fq2, Fq12> for Bn254

fn mul_013_by_013(l0: &EvaluatedLine<Fq2>, l1: &EvaluatedLine<Fq2>) -> [Fq2; 5]

Multiplies two lines in 013-form to get an element in 01234-form

fn mul_by_013(f: &Fq12, l: &EvaluatedLine<Fq2>) -> Fq12

Multiplies a line in 013-form with a Fp12 element to get an Fp12 element

fn mul_by_01234(f: &Fq12, x: &[Fq2; 5]) -> Fq12

Multiplies a line in 01234-form with a Fp12 element to get an Fp12 element

impl MillerStep for Bn254

fn miller_double_step( s: &AffinePoint<Self::Fp2>, ) -> (AffinePoint<Self::Fp2>, UnevaluatedLine<Self::Fp2>)

Miller double step

fn miller_double_and_add_step( s: &AffinePoint<Self::Fp2>, q: &AffinePoint<Self::Fp2>, ) -> (AffinePoint<Self::Fp2>, UnevaluatedLine<Self::Fp2>, UnevaluatedLine<Self::Fp2>)

Miller double and add step (2S + Q implemented as S + Q + S for efficiency)

type Fp2 = Fq2

fn miller_add_step( s: &AffinePoint<Self::Fp2>, q: &AffinePoint<Self::Fp2>, ) -> (AffinePoint<Self::Fp2>, UnevaluatedLine<Self::Fp2>)

Miller add step

impl MultiMillerLoop for Bn254

const SEED_ABS: u64 = 4_965_661_367_192_848_881u64

const PSEUDO_BINARY_ENCODING: &[i8] = _

type Fp = Fq

type Fp12 = Fq12

fn evaluate_lines_vec(f: Fq12, lines: Vec<EvaluatedLine<Fq2>>) -> Fq12

Function to evaluate the line functions of the Miller loop

fn pre_loop( Q_acc: Vec<AffinePoint<Fq2>>, _Q: &[AffinePoint<Fq2>], c: Option<Fq12>, xy_fracs: &[(Fq, Fq)], ) -> (Fq12, Vec<AffinePoint<Fq2>>)

Runs before the main loop in the Miller loop function

fn post_loop( f: &Fq12, Q_acc: Vec<AffinePoint<Fq2>>, Q: &[AffinePoint<Fq2>], _c: Option<Fq12>, xy_fracs: &[(Fq, Fq)], ) -> (Fq12, Vec<AffinePoint<Fq2>>)

Runs after the main loop in the Miller loop function

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