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Copy pathtaps_point_ops.rs
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taps_point_ops.rs
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use crate::bigint::U256;
use crate::bn254::fq12::Fq12;
use crate::bn254::fq2::Fq2;
use crate::bn254::fq6::Fq6;
use crate::bn254::g2::{
hinted_affine_add_line, hinted_affine_double_line, hinted_check_line_through_point,
hinted_check_tangent_line_keep_elements, hinted_ell_by_constant_affine,
hinted_mul_by_char_on_phi_q, hinted_mul_by_char_on_q, G2Affine,
};
use crate::bn254::utils::*;
use crate::chunk::taps_mul::{utils_fq6_sd_mul, utils_fq6_ss_mul};
use crate::{
bn254::{fp254impl::Fp254Impl, fq::Fq},
treepp::*,
};
use ark_ec::{AffineRepr, CurveGroup};
use ark_ff::{AdditiveGroup, Field, Fp12Config, PrimeField};
use num_bigint::BigUint;
use std::ops::Neg;
use std::str::FromStr;
use super::elements::{ElemG2Eval, ElementType};
use super::helpers::extern_nibbles_to_limbs;
use super::taps_mul::utils_multiply_by_line_eval;
use super::wrap_hasher::hash_messages;
// [q1, -q2, q3]
pub(crate) fn frob_q_power(q: ark_bn254::G2Affine, ate: i8) -> ark_bn254::G2Affine {
let beta_12x = BigUint::from_str(
"21575463638280843010398324269430826099269044274347216827212613867836435027261",
)
.unwrap();
let beta_12y = BigUint::from_str(
"10307601595873709700152284273816112264069230130616436755625194854815875713954",
)
.unwrap();
let beta_12 = ark_bn254::Fq2::from_base_prime_field_elems([
ark_bn254::Fq::from(beta_12x.clone()),
ark_bn254::Fq::from(beta_12y.clone()),
])
.unwrap();
let beta_13x = BigUint::from_str(
"2821565182194536844548159561693502659359617185244120367078079554186484126554",
)
.unwrap();
let beta_13y = BigUint::from_str(
"3505843767911556378687030309984248845540243509899259641013678093033130930403",
)
.unwrap();
let beta_13 = ark_bn254::Fq2::from_base_prime_field_elems([
ark_bn254::Fq::from(beta_13x.clone()),
ark_bn254::Fq::from(beta_13y.clone()),
])
.unwrap();
let beta_22x = BigUint::from_str(
"21888242871839275220042445260109153167277707414472061641714758635765020556616",
)
.unwrap();
let beta_22y = BigUint::from_str("0").unwrap();
let beta_22 = ark_bn254::Fq2::from_base_prime_field_elems([
ark_bn254::Fq::from(beta_22x.clone()),
ark_bn254::Fq::from(beta_22y.clone()),
])
.unwrap();
let beta_32x = BigUint::from_str(
"3772000881919853776433695186713858239009073593817195771773381919316419345261",
)
.unwrap();
let beta_32y = BigUint::from_str(
"2236595495967245188281701248203181795121068902605861227855261137820944008926",
)
.unwrap();
let beta_32 = ark_bn254::Fq2::from_base_prime_field_elems([
ark_bn254::Fq::from(beta_32x.clone()),
ark_bn254::Fq::from(beta_32y.clone()),
])
.unwrap();
let beta_33x = BigUint::from_str(
"19066677689644738377698246183563772429336693972053703295610958340458742082029",
)
.unwrap();
let beta_33y = BigUint::from_str(
"18382399103927718843559375435273026243156067647398564021675359801612095278180",
)
.unwrap();
let beta_33 = ark_bn254::Fq2::from_base_prime_field_elems([
ark_bn254::Fq::from(beta_33x.clone()),
ark_bn254::Fq::from(beta_33y.clone()),
])
.unwrap();
let mut qq = q;
if ate == 1 {
qq.x.conjugate_in_place();
qq.x *= beta_12;
qq.y.conjugate_in_place();
qq.y *= beta_13; // = phi(q)
} else if ate == -1 {
qq.x *= beta_22; // = - phi(phi(q))
} else if ate == 3 {
qq.x.conjugate_in_place();
qq.x *= beta_32;
qq.y.conjugate_in_place();
qq.y *= beta_33; // = phi(phi(phi(q)))
}
qq
}
fn utils_point_double_eval(
t: ark_bn254::G2Affine,
p: ark_bn254::G1Affine,
) -> (
(ark_bn254::G2Affine, (ark_bn254::Fq2, ark_bn254::Fq2)),
Script,
Vec<Hint>,
) {
let mut hints = vec![];
let t_is_zero = t.is_zero()
|| (t == ark_bn254::G2Affine::new_unchecked(ark_bn254::Fq2::ZERO, ark_bn254::Fq2::ZERO)); // t is none or Some(0)
let is_valid_input = !t_is_zero;
let (alpha, bias) = if is_valid_input {
let alpha = (t.x.square() + t.x.square() + t.x.square()) / (t.y + t.y);
let bias = t.y - alpha * t.x;
(alpha, bias)
} else {
(ark_bn254::Fq2::ZERO, ark_bn254::Fq2::ZERO)
};
let (hinted_script1, hint1) = hinted_check_tangent_line_keep_elements(t, alpha, -bias);
let (hinted_script2, hint2) = hinted_affine_double_line(t.x, alpha, -bias);
let (hinted_script3, hint3) = hinted_ell_by_constant_affine(p.x, p.y, alpha, -bias);
let result = if is_valid_input {
let mut dbl_le0 = alpha;
dbl_le0.mul_assign_by_fp(&p.x);
let mut dbl_le1 = -bias;
dbl_le1.mul_assign_by_fp(&p.y);
((t + t).into_affine(), (dbl_le0, dbl_le1))
} else {
let zero_pt =
ark_bn254::G2Affine::new_unchecked(ark_bn254::Fq2::ZERO, ark_bn254::Fq2::ZERO);
(zero_pt, (ark_bn254::Fq2::ZERO, ark_bn254::Fq2::ZERO))
};
if is_valid_input {
hints.push(Hint::Fq(alpha.c0));
hints.push(Hint::Fq(alpha.c1));
hints.push(Hint::Fq(-bias.c0));
hints.push(Hint::Fq(-bias.c1));
hints.extend(hint1);
hints.extend(hint2);
hints.extend(hint3);
}
let script = script! {
// tx, ty, px, py
{ Fq2::toaltstack()}
{ G2Affine::is_zero_keep_element() } // ... (dependent on input), x, y, 0/1
OP_IF
// [t] [p]
{Fq2::fromaltstack()} {Fq2::drop()}
// [t]
{Fq2::push(ark_bn254::Fq2::ZERO)}
{Fq2::push(ark_bn254::Fq2::ZERO)}
// [t, nt]
{Fq2::push(ark_bn254::Fq2::ZERO)}
{Fq2::push(ark_bn254::Fq2::ZERO)}
// [t, nt, le]
OP_ELSE
// c3 (alpha), c4 (-bias), ... (other hints), x, y
for _ in 0..Fq::N_LIMBS * 2 {
OP_DEPTH OP_1SUB OP_ROLL
} // -bias, ..., x, y, alpha
for _ in 0..Fq::N_LIMBS * 2 {
OP_DEPTH OP_1SUB OP_ROLL
}
// [tx ty a b]
{Fq2::roll(6)} {Fq2::roll(6)} // alpha, -bias, x, y
// [a b tx ty]
{ hinted_script1 }
// [a b tx ty]
{Fq2::roll(6)} {Fq2::roll(6)}
// [tx ty a b]
{ Fq2::copy(2) } {Fq2::copy(2)}
// [tx ty a b a b]
{ Fq2::copy(10) }
// [tx ty a b a b tx]
{ hinted_script2 } // x, y, alpha, -bias, c3, c4 x', y'
{Fq2::toaltstack()} {Fq2::toaltstack()}
{Fq2::drop()} {Fq2::drop()}
{Fq2::fromaltstack()} {Fq2::fromaltstack()}
{Fq2::fromaltstack()} // x, y, alpha, -bias, x', y', px, py
{Fq2::roll(4)} {Fq2::roll(4)} // x, y, alpha, -bias, px, py, x', y'
{Fq2::toaltstack()} {Fq2::toaltstack()}
{ hinted_script3 } // x, y, le,
{Fq2::fromaltstack()} {Fq2::fromaltstack()} // x, y, le0, le1, x', y'
{Fq2::roll(6)} {Fq2::roll(6)} // x, y, x', y', le
OP_ENDIF
// [tx, ty, x', y', le0, le1]
};
(result, script, hints)
}
fn utils_point_add_eval(
t: ark_bn254::G2Affine,
q4: ark_bn254::G2Affine,
p: ark_bn254::G1Affine,
is_frob: bool,
ate_bit: i8,
) -> (
(ark_bn254::G2Affine, (ark_bn254::Fq2, ark_bn254::Fq2)),
Script,
Vec<Hint>,
) {
let mut hints = vec![];
// Precompute Q
let temp_q = q4;
let (qq, precomp_q_scr, precomp_q_hint) = if is_frob {
if ate_bit == 1 {
hinted_mul_by_char_on_q(temp_q)
} else {
hinted_mul_by_char_on_phi_q(temp_q)
}
} else if ate_bit == -1 {
(
temp_q.neg(),
script! {
// [q4]
{Fq::toaltstack()}
{Fq::neg(0)}
{Fq::fromaltstack()}
{Fq::neg(0)}
// [-q4]
},
vec![],
)
} else {
(temp_q, script! {}, vec![])
};
hints.extend(precomp_q_hint);
// Point Add
let t_is_zero = t.is_zero()
|| (t == ark_bn254::G2Affine::new_unchecked(ark_bn254::Fq2::ZERO, ark_bn254::Fq2::ZERO)); // t is none or Some(0)
let q_is_zero = qq.is_zero()
|| (qq == ark_bn254::G2Affine::new_unchecked(ark_bn254::Fq2::ZERO, ark_bn254::Fq2::ZERO)); // q is none or Some(0)
let is_valid_input = !t_is_zero && !q_is_zero && t != -qq;
// if it's valid input, you can compute line coefficients, else hardcode degenerate values
let (alpha, bias) = if is_valid_input {
if t == qq {
let alpha = (t.x.square() + t.x.square() + t.x.square()) / (t.y + t.y);
let bias = t.y - alpha * t.x;
(alpha, bias)
} else {
let alpha = (t.y - qq.y) / (t.x - qq.x);
let bias = t.y - alpha * t.x;
(alpha, bias)
}
} else {
(ark_bn254::Fq2::ZERO, ark_bn254::Fq2::ZERO)
};
let (hinted_script11, hint11) = hinted_check_line_through_point(t.x, alpha, -bias); // todo: remove unused arg: bias
let (hinted_script12, hint12) = hinted_check_line_through_point(qq.x, alpha, -bias); // todo: remove unused arg: bias
let (hinted_script2, hint2) = hinted_affine_add_line(t.x, qq.x, alpha, -bias);
let (hinted_script3, hint3) = hinted_ell_by_constant_affine(p.x, p.y, alpha, -bias);
// if it's valid input, you can compute result, else degenerate values
let result = if is_valid_input {
let mut add_le0 = alpha;
add_le0.mul_assign_by_fp(&p.x);
let mut add_le1 = -bias;
add_le1.mul_assign_by_fp(&p.y);
((t + qq).into_affine(), (add_le0, add_le1))
} else {
let zero_pt =
ark_bn254::G2Affine::new_unchecked(ark_bn254::Fq2::ZERO, ark_bn254::Fq2::ZERO);
(zero_pt, (ark_bn254::Fq2::ZERO, ark_bn254::Fq2::ZERO))
};
// if it's valid input, you need hints to run computation
if is_valid_input {
hints.push(Hint::Fq(alpha.c0));
hints.push(Hint::Fq(alpha.c1));
hints.push(Hint::Fq(-bias.c0));
hints.push(Hint::Fq(-bias.c1));
hints.extend(hint11);
hints.extend(hint12);
hints.extend(hint2);
hints.extend(hint3);
}
let drop_and_insert_zero = script! {
// [.., tx, ty, qx, qy], [px, py]
{ G2Affine::drop() }
{Fq2::fromaltstack()} {Fq2::drop()}
// [tx, ty]
{Fq2::push(ark_bn254::Fq2::ZERO)}
{Fq2::push(ark_bn254::Fq2::ZERO)}
// [t, nt]
{Fq2::push(ark_bn254::Fq2::ZERO)}
{Fq2::push(ark_bn254::Fq2::ZERO)}
// [t, nt, le]
};
let script = script! { // tx ty qx qy
// a, b, tx, ty, qx, qy, px, py
{Fq2::toaltstack()}
// [qx qy]
{precomp_q_scr}
// [qx qy]
{ G2Affine::is_zero_keep_element() }
OP_IF // q == 0
// [.., tx, ty, qx, qy], [px, py]
{drop_and_insert_zero.clone()}
OP_ELSE
// [t, q]
{ G2Affine::roll(1) }
{ G2Affine::is_zero_keep_element() }
OP_IF // t == 0
// [q, t]
{G2Affine::roll(1)}
{drop_and_insert_zero.clone()}
OP_ELSE
// qx qy tx ty
{G2Affine::copy(1)}
// qx qy tx ty qx qy
{ Fq2::neg(0)}
// qx qy tx ty qx -qy
{G2Affine::copy(1)}
// qx qy tx ty qx -qy tx ty
{G2Affine::equal()} // q = -t ?
// qx qy tx ty 0/1
OP_IF // q == -t
// [q, t]
{G2Affine::roll(1)}
// [t, q]
{drop_and_insert_zero}
OP_ELSE
// [qx, qy, tx, ty]
for _ in 0..Fq::N_LIMBS * 2 {
OP_DEPTH OP_1SUB OP_ROLL
}
for _ in 0..Fq::N_LIMBS * 2 {
OP_DEPTH OP_1SUB OP_ROLL
}
// [qx, qy, tx, ty, c3, c4]
{Fq2::roll(6)} {Fq2::roll(6)}
// [qx, qy, c3, c4, tx, ty]
{Fq2::copy(2)} {Fq2::copy(2)}
{Fq2::toaltstack()} {Fq2::toaltstack()}
// [qx, qy, c3, c4, tx, ty] [tx, y]
{hinted_script11}
// [qx, qy, c3, c4 ]
{Fq2::fromaltstack()} {Fq2::fromaltstack()}
// [qx, qy, c3, c4, tx, ty]
{Fq2::roll(6)} {Fq2::roll(6)}
// [qx, qy, tx, ty, c3, c4]
{ Fq2::copy(10) }
{ Fq2::roll(10) }
// [qx, tx, ty, c3, c4, qx, qy]
{ hinted_script12 }
// [qx, tx, ty, c3, c4]
{Fq2::copy(2)} {Fq2::copy(2)}
// [qx, tx, ty, c3, c4, c3, c4]
{ Fq2::copy(10) }
// [qx, tx, ty, c3, c4, c3, c4, tx]
{ Fq2::roll(14) }
// [tx, ty, c3, c4, c3, c4, tx, qx]
{ hinted_script2 }
// [tx, ty, c3, c4, c3, c4, x', y']
{Fq2::toaltstack()} {Fq2::toaltstack()}
{Fq2::drop()} {Fq2::drop()}
{Fq2::fromaltstack()} {Fq2::fromaltstack()}
// [tx, ty, c3, c4, x', y']
{Fq2::fromaltstack()}
// [tx, ty, c3, c4, x', y', px, py]
{Fq2::roll(4)} {Fq2::roll(4)}
// [tx, ty, c3, c4, px, py, x', y']
{Fq2::toaltstack()} {Fq2::toaltstack()}
// [tx, ty, c3, c4, px, py]
{ hinted_script3 }
// [tx, ty,le0, le1]
{Fq2::fromaltstack()} {Fq2::fromaltstack()}
// [tx, ty, le0, le1, x', y']
{Fq2::roll(6)} {Fq2::roll(6)}
// [tx, ty, x', y', le0, le1]
OP_ENDIF
// [tx, ty, x', y', le0, le1]
OP_ENDIF
OP_ENDIF
};
(result, script, hints)
}
#[allow(clippy::too_many_arguments)]
fn point_ops_and_multiply_line_evals_step_1(
is_dbl: bool,
is_frob: Option<bool>,
ate_bit: Option<i8>,
t4: ark_bn254::G2Affine,
p4: ark_bn254::G1Affine,
q4: Option<ark_bn254::G2Affine>,
p3: ark_bn254::G1Affine,
t3: ark_bn254::G2Affine,
q3: Option<ark_bn254::G2Affine>,
p2: ark_bn254::G1Affine,
t2: ark_bn254::G2Affine,
q2: Option<ark_bn254::G2Affine>,
) -> (ElemG2Eval, bool, Script, Vec<Hint>) {
// a, b, tx, ty, px, py
let ((nt, (le4_0, le4_1)), nt_scr, nt_hints) = if is_dbl {
//[a, b, tx, ty, px, py]
utils_point_double_eval(t4, p4)
} else {
// a, b, tx, ty, qx, qy, px, py
assert!(q4.is_some());
utils_point_add_eval(t4, q4.unwrap(), p4, is_frob.unwrap(), ate_bit.unwrap())
};
let le4 = ark_bn254::Fq6::new(le4_0, le4_1, ark_bn254::Fq2::ZERO);
let (alpha_t3, neg_bias_t3) = if is_dbl {
let alpha_t3 = (t3.x.square() + t3.x.square() + t3.x.square()) / (t3.y + t3.y);
let neg_bias_t3 = alpha_t3 * t3.x - t3.y;
(alpha_t3, neg_bias_t3)
} else {
let ate_bit = ate_bit.unwrap();
let is_frob = is_frob.unwrap();
let temp_q = q3.unwrap();
let q3 = if is_frob {
if ate_bit == 1 {
hinted_mul_by_char_on_q(temp_q).0
} else {
hinted_mul_by_char_on_phi_q(temp_q).0
}
} else if ate_bit == -1 {
temp_q.neg()
} else {
temp_q
};
let alpha_t3 = (t3.y - q3.y) / (t3.x - q3.x);
let neg_bias_t3 = alpha_t3 * t3.x - t3.y;
(alpha_t3, neg_bias_t3)
};
let (alpha_t2, neg_bias_t2) = if is_dbl {
let alpha_t2 = (t2.x.square() + t2.x.square() + t2.x.square()) / (t2.y + t2.y);
let neg_bias_t2 = alpha_t2 * t2.x - t2.y;
(alpha_t2, neg_bias_t2)
} else {
let ate_bit = ate_bit.unwrap();
let is_frob = is_frob.unwrap();
let temp_q = q2.unwrap();
let q2 = if is_frob {
if ate_bit == 1 {
hinted_mul_by_char_on_q(temp_q).0
} else {
hinted_mul_by_char_on_phi_q(temp_q).0
}
} else if ate_bit == -1 {
temp_q.neg()
} else {
temp_q
};
let alpha_t2 = (t2.y - q2.y) / (t2.x - q2.x);
let neg_bias_t2 = alpha_t2 * t2.x - t2.y;
(alpha_t2, neg_bias_t2)
};
let (g, fg_scr, fg_hints) = utils_multiply_by_line_eval(le4, alpha_t3, neg_bias_t3, p3);
let one_plus_fg_j_sq = (le4 * g * ark_bn254::Fq12Config::NONRESIDUE) + ark_bn254::Fq6::ONE;
let fpg = le4 + g;
let (hinted_ell_t2, hints_ell_t2) =
hinted_ell_by_constant_affine(p2.x, p2.y, alpha_t2, neg_bias_t2);
let mut t2le_a = alpha_t2;
t2le_a.mul_assign_by_fp(&p2.x);
let mut t2le_b = neg_bias_t2;
t2le_b.mul_assign_by_fp(&p2.y);
let mut t3le_a = alpha_t3;
t3le_a.mul_assign_by_fp(&p3.x);
let mut t3le_b = neg_bias_t3;
t3le_b.mul_assign_by_fp(&p3.y);
let mut hints = vec![];
hints.extend_from_slice(&nt_hints);
hints.extend_from_slice(&fg_hints);
hints.extend_from_slice(&hints_ell_t2);
let mul_by_beta_sq_scr = script! {
{Fq6::mul_fq2_by_nonresidue()}
{Fq2::roll(4)} {Fq2::roll(4)}
};
let ops_scr = script! {
// [hints, t4, (q4), p4, p3, p2]
{Fq2::toaltstack()}
{Fq2::copy(2)} {Fq2::toaltstack()}
{Fq2::toaltstack()}
// [hints, t4, (q4), p4] [p2, p4, p3]
{nt_scr}
// [hints, t4, nt4, le0, le1] [p2, p4, p3]
// [hints, t4, nt4, le] [p2, p4, p3]
{Fq2::fromaltstack()}
// [hints, t4, nt4, le, p3] [p2, p4]
{fg_scr}
// [t4, nt4, p3, g, f, fg] [p2, p4]
{mul_by_beta_sq_scr}
// [t4, nt4, p3, g, f, fg_beta_sq] [p2, p4]
{Fq6::push(ark_bn254::Fq6::ONE)}
{Fq6::add(6, 0)}
// [t4, nt4, p3, g, f, fg_beta_sq+1] [p2, p4]
// [t4, nt4, p3, g, f, fg'] [p2, p4]
{Fq6::toaltstack()}
// [t4, nt4, p3, g0, g1, f0, f1] [p2, p4, fg']
{Fq2::add(6, 2)}
{Fq2::add(4, 2)}
{Fq6::fromaltstack()}
// [t4, nt4, p3, g+f, fg'] [p2, p4]
{Fq2::fromaltstack()}
// [t4, nt4, p3, g+f, fg', p4] [p2]
{Fq2::fromaltstack()}
{Fq2::copy(0)}
{Fq2::push(alpha_t2)}
{Fq2::push(neg_bias_t2)}
// [t4, nt4, p3, g+f, fg', p4, p2, p2, a, b] []
{Fq2::roll(4)}
{hinted_ell_t2}
// [t4, nt4, p3, g+f, fg', p4, p2, p2le] []
};
// rearrange elements order
let rearrange_scr = script! {
// [t4, nt4, p3, g+f, fg', p4, p2, p2le]
{Fq6::toaltstack()}
{Fq2::roll(12)}
{Fq2::fromaltstack()}
// [t4, nt4, g+f, fg', p4, p3, p2] [p2le]
{Fq2::roll(18)} {Fq2::roll(18)}
// [t4, g+f, fg', p4, p3, p2, nt4] [p2le]
for _ in 0..5 {
{Fq2::roll(18)}
}
// [t4, p4, p3, p2, nt4, g+f, fg'] [p2le]
{Fq2::fromaltstack()} {Fq2::fromaltstack()}
// [t4, p4, p3, p2, nt4, g+f, fg', p2le]
};
// check if g+f == 0 || fg' == 0
let input_validity_scr = script! {
// [t4, p4, p3, p2, nt4, g+f, fg', p2le]
{Fq6::copy(4)}
// [t4, p4, p3, p2, nt4, g+f, fg', p2le, fg']
{Fq6::is_zero()} OP_NOT OP_TOALTSTACK // fg'_is_not_zero()
// [t4, p4, p3, p2, nt4, g+f, fg', p2le]
{Fq2::copy(16)} {Fq2::copy(16)}
// [t4, p4, p3, p2, nt4, g+f, fg', p2le, nt4]
{G2Affine::is_zero_keep_element()}
OP_NOT OP_TOALTSTACK
// [t4, p4, p3, p2, nt4, g+f, fg', p2le, nt4]
{G2Affine::drop()}
//[t4, p4, p3, p2, nt4, g+f, fg', p2le] [0/1, 0/1, 0/1]
OP_FROMALTSTACK OP_FROMALTSTACK
// [ .., nt4.is_not_zero() fg'_is_not_zero()] []
OP_BOOLAND
OP_IF
// none are zero
{1}
// [t4, p4, p3, p2, nt4, g+f, fg', p2le, {1}]
OP_ELSE
// at least one is zero
{0}
// [t4, p4, p3, p2, nt4, g+f, fg', p2le, {0}]
OP_ENDIF
// [t4, p4, p3, p2, nt4, g+f, fg', p2le, 0/1]
};
let scr = script! {
{ops_scr}
{rearrange_scr}
{input_validity_scr}
};
let hout = ElemG2Eval {
t: nt,
p2le: [t2le_a, t2le_b],
one_plus_ab_j_sq: one_plus_fg_j_sq,
a_plus_b: [fpg.c0, fpg.c1],
};
let input_is_valid = one_plus_fg_j_sq != ark_bn254::Fq6::ZERO
&& (nt != ark_bn254::G2Affine::zero()
&& nt
!= ark_bn254::G2Affine::new_unchecked(ark_bn254::Fq2::ZERO, ark_bn254::Fq2::ZERO));
(hout, input_is_valid, scr, hints)
}
#[allow(clippy::too_many_arguments)]
pub(crate) fn chunk_point_ops_and_multiply_line_evals_step_1(
is_dbl: bool,
is_frob: Option<bool>,
ate_bit: Option<i8>,
t4: ElemG2Eval,
p4: ark_bn254::G1Affine,
q4: Option<ark_bn254::G2Affine>,
p3: ark_bn254::G1Affine,
t3: ark_bn254::G2Affine,
q3: Option<ark_bn254::G2Affine>,
p2: ark_bn254::G1Affine,
t2: ark_bn254::G2Affine,
q2: Option<ark_bn254::G2Affine>,
) -> (ElemG2Eval, bool, Script, Vec<Hint>) {
let (hint_out, is_valid, ops_scr, hints) = point_ops_and_multiply_line_evals_step_1(
is_dbl, is_frob, ate_bit, t4.t, p4, q4, p3, t3, q3, p2, t2, q2,
);
let pre_hash_scr = script! {
// [t4, p4, p3, p2, nt4, F, 0/1] [outhash, p2hash, p3hash, p4hash, in_t4hash, ht4_le]
{Fq::fromaltstack()}
{9} OP_ROLL OP_TOALTSTACK
// [t4, p4, p3, p2, nt4, F, ht4_le] [outhash, p3hash, p4hash, in_t4hash, 0/1]
for _ in 0..(2+2+2+4+14) {
{Fq::roll(24)}
}
// [t4, ht4_le, p4, p3, p2, nt4, F] [outhash, p3hash, p4hash, in_t4hash, 0/1]
OP_FROMALTSTACK
// [t4, ht4_le, p4, p3, p2, nt4, F, 0/1] [outhash, p3hash, p4hash, in_t4hash]
};
let _hash_scr = script! {
// [t4, ht4_le, p4, p3, nt4, fg] [outhash, p3hash, p4hash, in_t4hash]
{hash_messages(vec![ElementType::G2EvalPoint, ElementType::G1, ElementType::G1, ElementType::G1, ElementType::G2Eval])}
};
let pre_ops_scr = script! {
// [hints, {t4, ht4_le}, p4, p3, p2] [outhash, p2hash, p3hash, p4hash, in_t4hash (q4)]
if !is_dbl {
// [hints, {t4, ht4_le}, p4, p3, p2] [outhash, p2hash, p3hash, p4hash, in_t4hash q4]
for _ in 0..4 {
{Fq::fromaltstack()} // q
}
// [hints, {t4, ht4_le}, p4, p3, p2, q4] [outhash, p2hash, p3hash, p4hash, in_t4hash]
{Fq::roll(10)} {Fq::toaltstack()}
// [hints, t4, p4, p3, p2, q4] [outhash, p2hash, p3hash, p4hash, in_t4hash, ht4_le]
{Fq6::roll(4)}
// [hints, t4, q4, p4, p3, p2] [outhash, p2hash, p3hash, p4hash, in_t4hash, ht4_le]
} else {
// [hints, {t4, ht4_le}, p4, p3, p2] [outhash, p2hash, p3hash, p4hash, in_t4hash, ht4_le]
{Fq::roll(6)} {Fq::toaltstack()}
// [hints, t4, p4, p3, p2] [outhash, p2hash, p3hash, p4hash, in_t4hash, ht4_le]
}
};
let scr = script! {
{pre_ops_scr}
// [hints, t4, (q4), p4, p3, p2] [outhash, p2hash, p3hash, p4hash, in_t4hash, ht4_le]
{ops_scr}
// [t4, p4, p3, p2, nt4, F, 0/1] [outhash, p2hash, p3hash, p4hash, in_t4hash, ht4_le]
{pre_hash_scr}
// [t4, in_t4hash, p4, p3, p2, nt4, F, 0/1] [outhash, p3hash, p4hash, in_t4hash]
// {hash_scr}
};
(hint_out, is_valid, scr, hints)
}
pub(crate) fn chunk_point_ops_and_multiply_line_evals_step_2(
f: ElemG2Eval,
) -> (ark_bn254::Fq6, bool, Script, Vec<Hint>) {
let (ops_res, is_valid_input, ops_scr, ops_hints) = point_ops_and_multiply_line_evals_step_2(f);
let scr = script! {
// [hints, apb, Ab, c, Haux_in, h] [hash_h, hash_in]
{Fq::roll(6)} {Fq::toaltstack()}
// [hints, {apb, Ab, c}, h] [hash_h, hash_in, Haux_in]
{ops_scr}
// [{apb, Ab, c}, h, 0/1] [hash_h, hash_in, Haux_in]
{Fq::fromaltstack()}
// [{apb, Ab, c}, h, 0/1 Haux_in] [hash_h, hash_in]
{9} OP_ROLL OP_TOALTSTACK
// [{apb, Ab, c}, h, Haux_in] [hash_h, hash_in, 0/1]
{Fq6::roll(1)} OP_FROMALTSTACK
// [{apb, Ab, c, Haux_in}, h, 0/1] [hash_h, hash_in]
};
let _hash_scr = script! {
// [t4, ht4_le, p4, p3, nt4, fg] [outhash, p3hash, p4hash, in_t4hash]
{hash_messages(vec![ElementType::G2EvalMul, ElementType::Fp6])}
OP_TRUE
};
(ops_res, is_valid_input, scr, ops_hints)
}
pub(crate) fn point_ops_and_multiply_line_evals_step_2(
f: ElemG2Eval,
) -> (ark_bn254::Fq6, bool, Script, Vec<Hint>) {
let ab = f.one_plus_ab_j_sq;
let apb = ark_bn254::Fq6::new(f.a_plus_b[0], f.a_plus_b[1], ark_bn254::Fq2::ZERO);
assert_ne!(ab, ark_bn254::Fq6::ZERO);
let le2_c1 = ark_bn254::Fq6::new(f.p2le[0], f.p2le[1], ark_bn254::Fq2::ZERO);
let le2 = ark_bn254::Fq12::new(ark_bn254::Fq6::ONE, le2_c1);
let le4_mul_le3 = ark_bn254::Fq12::new(ark_bn254::Fq6::ONE, apb / ab);
let le4_mul_le3_mul_le2 = le4_mul_le3 * le2;
let abc = ab * le2_c1;
let numerator = apb + abc;
let apb_mul_c = le2_c1 * apb;
let denom = ab + apb_mul_c * ark_bn254::Fq12Config::NONRESIDUE;
let (abc_out, abc_scr, abc_hints) = utils_fq6_sd_mul(ab, le2_c1);
assert_eq!(abc_out, ab * le2_c1);
let (apb_mul_c_out, apb_mul_c_scr, apb_mul_c_hints) = utils_fq6_ss_mul(apb, le2_c1);
assert_eq!(apb_mul_c, apb_mul_c_out);
let mut hints = vec![];
hints.extend_from_slice(&abc_hints);
hints.extend_from_slice(&apb_mul_c_hints);
let mock_output = ark_bn254::Fq6::ONE;
let is_valid_input = denom != ark_bn254::Fq6::ZERO;
let (g, den_mul_h_scr) = if is_valid_input {
let g = le4_mul_le3_mul_le2.c1 / le4_mul_le3_mul_le2.c0;
assert_eq!(g * denom, numerator);
let (den_mul_h_scr, den_mul_h_hints) = Fq6::hinted_mul_keep_elements(6, denom, 0, g);
hints.extend_from_slice(&den_mul_h_hints);
(g, den_mul_h_scr)
} else {
let den_mul_h_scr =
Fq6::hinted_mul_keep_elements(6, ark_bn254::Fq6::ONE, 0, ark_bn254::Fq6::ONE).0;
(mock_output, den_mul_h_scr)
};
let mul_by_beta_sq_scr = script! {
{Fq6::mul_fq2_by_nonresidue()}
{Fq2::roll(4)} {Fq2::roll(4)}
};
let scr = script! {
{Fq6::toaltstack()}
// [hints, apb, Ab, c] [h]
{abc_scr}
// [hints, apb, Ab, c, Abc] [h]
// [hints, apb, Ab, c, Abc] [h]
{Fq2::copy(18)} {Fq2::copy(18)}
// [hints, apb, Ab, c, Abc, apb] [h]
{Fq2::copy(12)} {Fq2::copy(12)}
// [hints, apb, Ab, c, Abc, apb, c] [h]
{apb_mul_c_scr}
// [hints, apb, Ab, c, Abc, apb, c, Apb_mul_C] [h]
{mul_by_beta_sq_scr}
// [hints, apb, Ab, c, Abc, apb, c, Apb_mul_C_beta_sq] [h]
{Fq6::copy(24)}
// [hints, apb, Ab, c, Abc, apb, c, Apb_mul_C_beta_sq, Ab] [h]
{Fq6::add(6, 0)}
// [hints, apb, Ab, c, Abc, apb, c, denom] [h]
{Fq6::toaltstack()}
// [hints, apb, Ab, c, Abc, apb, c] [h, denom]
{Fq2::drop()} {Fq2::drop()}
// [hints, apb, Ab, c, Abc, apb] [h, denom]
{Fq2::push(ark_bn254::Fq2::ZERO)}
{Fq6::add(6, 0)}
// [hints, apb, Ab, c, numerator] [h, denom]
{Fq6::fromaltstack()}
// [hints, apb, Ab, c, numerator, denom] [h]
{Fq6::copy(0)} {Fq6::is_zero()} OP_NOT // denom_is_not_zero
OP_IF
// [hints, apb, Ab, c, numerator, denom] [h]
{Fq6::fromaltstack()}
// [hints, apb, Ab, c, numerator, denom, h]
{den_mul_h_scr}
// [hints, apb, Ab, c, numerator, denom, h, denom_mul_h]
{Fq12::roll(12)}
// [hints, apb, Ab, c, h, denom_mul_h, numerator, denom]
{Fq6::drop()}
// [apb, Ab, c, h, denom_mul_h, numerator]
{Fq6::equalverify()}
// [ apb, Ab, c, h ]
{1} // input was valid
// [ apb, Ab, c, h, 1]
OP_ELSE
// any of the inputs was invalid
// [ apb, Ab, c, numerator, denom] [h]
{Fq6::drop()} {Fq6::drop()} {Fq6::fromaltstack()}
// [apb, Ab, c, h]
{Fq6::drop()}
{Fq6::push(mock_output)}
// [apb, Ab, c, mock_h]
{0} // input was invalid
OP_ENDIF
// [ apb, Ab, c, h, 0/1]
};
(g, is_valid_input, scr, hints)
}
pub(crate) fn chunk_init_t4(ts: [ark_ff::BigInt<4>; 4]) -> (ElemG2Eval, bool, Script, Vec<Hint>) {
let mut hints = vec![];
let mock_t = ark_bn254::G2Affine::new_unchecked(ark_bn254::Fq2::ONE, ark_bn254::Fq2::ONE);
let are_valid_fps = ts.iter().filter(|f| **f < ark_bn254::Fq::MODULUS).count() == ts.len();
let mut t4: ElemG2Eval = ElemG2Eval {
t: mock_t,
p2le: [ark_bn254::Fq2::ZERO; 2],
one_plus_ab_j_sq: ark_bn254::Fq6::ZERO,
a_plus_b: [ark_bn254::Fq2::ZERO; 2],
};
if are_valid_fps {
t4.t = ark_bn254::G2Affine::new_unchecked(
ark_bn254::Fq2::new(ts[0].into(), ts[1].into()),
ark_bn254::Fq2::new(ts[2].into(), ts[3].into()),
);
}
let (on_curve_scr, on_curve_hints) = G2Affine::hinted_is_on_curve(t4.t.x, t4.t.y);
if are_valid_fps {
hints.extend_from_slice(&on_curve_hints);
}
let is_valid_input = are_valid_fps && t4.t.is_on_curve();
let aux_hash_le = t4.hash_le(); // aux_hash_le doesn't include t4.t, is constant, so hash_le can be hardcoded
let ops_scr = script! {
// [hints] [f_hash_claim, y1, y0, x1, x0]
for _ in 0..4 {
{Fq::fromaltstack()}
}
{Fq2::copy(2)} {Fq2::copy(2)}
for _ in 0..4 {
{ Fq::push_hex(Fq::MODULUS) }
{ U256::lessthan(1, 0) } // a < p
OP_TOALTSTACK
}
{1}
for _ in 0..4 {
OP_FROMALTSTACK
OP_BOOLAND
}
OP_IF
// [hints, x0, x1, y0, y1] [f_hash_claim]
{Fq2::copy(2)} {Fq2::copy(2)}
// [hints, x0, x1, y0, y1, x0, x1, y0, y1] [f_hash_claim]
{on_curve_scr}
OP_IF
// [x0, x1, y0, y1] [f_hash_claim]
for le in extern_nibbles_to_limbs(aux_hash_le) {
{le}
}
// [x0, x1, y0, y1, aux_hash_le] [f_hash_claim]
{1}
OP_ELSE
for _ in 0..4 {
{Fq::drop()}
}
{G2Affine::push(mock_t)}
// [mock_t] [f_hash_claim]
for le in extern_nibbles_to_limbs(aux_hash_le) {
{le}
}
// [mock_t, aux_hash_le] [f_hash_claim]
{0}
OP_ENDIF
// [T4, HashT4Aux, {0/1}] [NT4_hash_claim]
OP_ELSE
// [x0, x1, y0, y1] [f_hash_claim]
for _ in 0..4 {
{Fq::drop()}
}
{G2Affine::push(mock_t)}
for le in extern_nibbles_to_limbs(aux_hash_le) {
{le}
}
// [mock_t, aux_hash_le] [f_hash_claim]
{0}
OP_ENDIF
};
let _hash_scr = script! {
{hash_messages(vec![ElementType::G2EvalPoint])}
OP_TRUE
};
(t4, is_valid_input, ops_scr, hints)
}
#[cfg(test)]
mod test {
use std::str::FromStr;
use crate::{
bn254::{
fp254impl::Fp254Impl, fq::Fq, fq2::Fq2, fq6::Fq6, g1::G1Affine, g2::G2Affine,
utils::Hint,
},
chunk::{
elements::{DataType, ElemG2Eval, ElementType},
taps_point_ops::{
chunk_init_t4, chunk_point_ops_and_multiply_line_evals_step_1,
chunk_point_ops_and_multiply_line_evals_step_2,
point_ops_and_multiply_line_evals_step_1, point_ops_and_multiply_line_evals_step_2,
utils_point_add_eval,
},
wrap_hasher::hash_messages,
},
execute_script,
};
use ark_ec::AffineRepr;
use ark_ff::{AdditiveGroup, BigInt, Field, UniformRand};
use bitcoin_script::script;
use num_bigint::BigUint;
use rand::SeedableRng;
use rand_chacha::ChaCha20Rng;
use super::{frob_q_power, utils_point_double_eval};
#[test]
fn test_point_double_eval() {
let mut prng = ChaCha20Rng::seed_from_u64(0);
let t = ark_bn254::G2Affine::rand(&mut prng);
let p = ark_bn254::G1Affine::rand(&mut prng);
let ((r, le), scr, hints) = utils_point_double_eval(t, p);
// a, b, tx, ty, px, py
let script = script! {
for h in hints {
{h.push()}
}
{G2Affine::push(t)}
{G1Affine::push(p)}
// [hints, tx, ty, px, py]
{scr}
// t, R, dbl_le
{Fq2::push(le.1)}
{Fq2::equalverify()}
{Fq2::push(le.0)}
{Fq2::equalverify()}
{Fq2::push(r.y)}
{Fq2::equalverify()}
{Fq2::push(r.x)}
{Fq2::equalverify()}
{Fq2::push(t.y)}
{Fq2::equalverify()}
{Fq2::push(t.x)}
{Fq2::equalverify()}
OP_TRUE
};
let res = execute_script(script);
if res.final_stack.len() > 1 {
for i in 0..res.final_stack.len() {
println!("{i:} {:?}", res.final_stack.get(i));
}
}
assert!(res.success);
assert!(res.final_stack.len() == 1);
println!(
"utils_point_double_eval disprovable(false) max_stack {:?}",
res.stats.max_nb_stack_items
);
}
#[test]
fn test_point_add_eval() {
let mut prng = ChaCha20Rng::seed_from_u64(0);
let t = ark_bn254::G2Affine::rand(&mut prng);
let q = ark_bn254::G2Affine::rand(&mut prng);
let p = ark_bn254::G1Affine::rand(&mut prng);
let beta_22x = BigUint::from_str(
"21888242871839275220042445260109153167277707414472061641714758635765020556616",
)
.unwrap();
let beta_22y = BigUint::from_str("0").unwrap();