Function utils_multiply_by_line_eval

bitvm/src/chunk/taps_mul.rs:151–193

Given line evaluation f, line coeff (alpha_t3, neg_bias_t3) and point P3, Compute line evaluation 'g' at P3 and multiply it with f. Return Script and Hints for the computation and return the line evaluation g. Compute g = le_{t3} (P3); h = f * g; Return (g, Script(Compute), Hints(Compute))

(
    f: ark_bn254::Fq6,
    alpha_t3: ark_bn254::Fq2,
    neg_bias_t3: ark_bn254::Fq2,
    p3: ark_bn254::G1Affine,
)

/// Compute g = le_{t3} (P3); h = f * g;
/// Return (g, Script(Compute), Hints(Compute))
pub(crate) fn utils_multiply_by_line_eval(
    f: ark_bn254::Fq6,
    alpha_t3: ark_bn254::Fq2,
    neg_bias_t3: ark_bn254::Fq2,
    p3: ark_bn254::G1Affine,
) -> (ark_bn254::Fq6, Script, Vec<Hint>) {
    assert_eq!(f.c2, ark_bn254::Fq2::ZERO);

    let mut l0_t3 = alpha_t3;
    l0_t3.mul_assign_by_fp(&p3.x);
    let mut l1_t3 = neg_bias_t3;
    l1_t3.mul_assign_by_fp(&p3.y);

    let (hinted_ell_t3, hints_ell_t3) =
        hinted_ell_by_constant_affine(p3.x, p3.y, alpha_t3, neg_bias_t3);

    let g = ark_bn254::Fq6::new(l0_t3, l1_t3, ark_bn254::Fq2::ZERO);
    let (_, fg_scr, fg_hints) = utils_fq6_ss_mul(g, f);

    let scr = script! {
        // [f, p3]
        {Fq2::copy(0)}
        // [f, p3, p3]
        {Fq2::push(alpha_t3)}
        {Fq2::push(neg_bias_t3)}
        // [f, p3, p3, a, b]
        {Fq2::roll(4)}
        // [f, p3, a, b, p3]
        {hinted_ell_t3}
        // [f, p3, le0, le1]
        // [f, p3, g]
        {Fq2::roll(8)} {Fq2::roll(8)}
        // [p3, g, f]
        {fg_scr}
        // [p3, g, f, fg]
    };

    let mut hints = vec![];
    hints.extend_from_slice(&hints_ell_t3);
    hints.extend_from_slice(&fg_hints);

    (g, scr, hints)
}

/// Compute product of two Fq12 elements in normalized form (1 + c J) <- (1 + a J) x (1 + b J).
/// Input a, b and output c.