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g16_runner_core.rs
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use crate::chunk::{
elements::CompressedStateObject, g16_runner_utils::*, taps_point_ops::frob_q_power,
};
use ark_ec::CurveGroup;
use ark_ff::{Field, PrimeField};
use bitcoin::ScriptBuf;
use super::{
api::NUM_PUBS,
api_compiletime_utils::ATE_LOOP_COUNT,
elements::{DataType, ElementType, HashBytes},
};
#[derive(Debug)]
pub struct PublicParams {
pub q2: ark_bn254::G2Affine,
pub q3: ark_bn254::G2Affine,
pub fixed_acc: ark_bn254::Fq6, // precomputable fp12 accumulator from fixed pairing arguments
pub ks_vks: Vec<ark_bn254::G1Affine>,
pub vky0: ark_bn254::G1Affine,
}
#[derive(Debug)]
pub(crate) struct InputProof {
pub(crate) p2: ark_bn254::G1Affine,
pub(crate) p4: ark_bn254::G1Affine,
pub(crate) q4: ark_bn254::G2Affine,
pub(crate) c: ark_bn254::Fq6,
pub(crate) ks: Vec<ark_bn254::Fr>,
}
impl InputProof {
pub(crate) fn to_raw(&self) -> InputProofRaw {
let p2x = self.p2.x.into_bigint();
let p2y = self.p2.y.into_bigint();
let p4x = self.p4.x.into_bigint();
let p4y = self.p4.y.into_bigint();
let q4x0 = self.q4.x.c0.into_bigint();
let q4x1 = self.q4.x.c1.into_bigint();
let q4y0 = self.q4.y.c0.into_bigint();
let q4y1 = self.q4.y.c1.into_bigint();
let c: Vec<ark_ff::BigInt<4>> = self
.c
.to_base_prime_field_elements()
.map(|f| f.into_bigint())
.collect();
let ks: Vec<ark_ff::BigInt<4>> = self.ks.iter().map(|f| f.into_bigint()).collect();
InputProofRaw {
p2: [p2x, p2y],
p4: [p4x, p4y],
q4: [q4x0, q4x1, q4y0, q4y1],
c: c.try_into().unwrap(),
ks: ks.try_into().unwrap(),
}
}
}
#[derive(Debug)]
pub(crate) struct InputProofRaw {
pub(crate) p2: [ark_ff::BigInt<4>; 2],
pub(crate) p4: [ark_ff::BigInt<4>; 2],
pub(crate) q4: [ark_ff::BigInt<4>; 4],
pub(crate) c: [ark_ff::BigInt<4>; 6],
pub(crate) ks: [ark_ff::BigInt<4>; NUM_PUBS],
}
fn compare(hint_out: &DataType, claimed_assertions: &mut Option<Vec<HashBytes>>) -> Option<bool> {
if claimed_assertions.is_none() {
return None;
}
assert!(!hint_out.output_is_field_element());
let hint_out_hash = hint_out.to_hash();
let matches = if let CompressedStateObject::Hash(hash) = hint_out_hash {
if let Some(claimed_assertions) = claimed_assertions {
claimed_assertions.pop().unwrap() == hash
} else {
unreachable!(); // verified that claimed_assertions is_some()
}
} else {
unreachable!(); // verified that hint_out is hash above
};
Some(matches)
}
pub(crate) fn groth16_generate_segments(
skip_evaluation: bool,
all_output_hints: &mut Vec<Segment>,
eval_ins: InputProofRaw,
pubs: PublicParams,
claimed_assertions: &mut Option<Vec<HashBytes>>,
) -> bool {
macro_rules! push_compare_or_return {
($seg:ident) => {{
all_output_hints.push($seg.clone());
if $seg.scr_type.is_final_script() {
if let DataType::U256Data(felem) = $seg.result.0 {
if felem != ark_ff::BigInt::<4>::one() {
return false;
}
} else {
unreachable!();
}
} else if $seg.is_valid_input == false {
return false;
} else {
let matches = compare(&$seg.result.0, claimed_assertions);
if matches.is_some() && matches.unwrap() == false {
return false;
}
}
}};
}
let vky = pubs.ks_vks;
let vky0 = pubs.vky0;
let (gp2, gp4, gq4, gc, pub_scalars) = raw_input_proof_to_segments(eval_ins, all_output_hints);
let (gp2x, gp2y) = (gp2[0].clone(), gp2[1].clone());
let (gp4x, gp4y) = (gp4[0].clone(), gp4[1].clone());
let (q4xc0, q4xc1, q4yc0, q4yc1) = (
gq4[0].clone(),
gq4[1].clone(),
gq4[2].clone(),
gq4[3].clone(),
);
let gc = gc.to_vec();
let pub_scalars = pub_scalars.to_vec();
let p4 = wrap_hints_precompute_p(skip_evaluation, all_output_hints.len(), &gp4y, &gp4x);
push_compare_or_return!(p4);
let p2 = wrap_hints_precompute_p(skip_evaluation, all_output_hints.len(), &gp2y, &gp2x);
push_compare_or_return!(p2);
let msms = wrap_hint_msm(
skip_evaluation,
all_output_hints.len(),
pub_scalars.clone(),
vky.clone(),
);
for msm in &msms {
push_compare_or_return!(msm);
}
let p_vk0 = wrap_hint_hash_p(
skip_evaluation,
all_output_hints.len(),
&msms[msms.len() - 1],
vky0,
);
push_compare_or_return!(p_vk0);
let p3 = wrap_hints_precompute_p_from_hash(skip_evaluation, all_output_hints.len(), &p_vk0);
push_compare_or_return!(p3);
let c = wrap_hint_hash_c(skip_evaluation, all_output_hints.len(), gc.clone());
push_compare_or_return!(c);
let gcinv = wrap_hint_hash_c_inv(skip_evaluation, all_output_hints.len(), gc);
push_compare_or_return!(gcinv);
let mut t4 = wrap_hint_init_t4(
skip_evaluation,
all_output_hints.len(),
&q4yc1,
&q4yc0,
&q4xc1,
&q4xc0,
);
push_compare_or_return!(t4);
let (mut t2, mut t3) = (pubs.q2, pubs.q3);
let mut f_acc = gcinv.clone();
for j in (1..ATE_LOOP_COUNT.len()).rev() {
if !skip_evaluation {
println!("Processing {:?}-th iteration of Miller Loop", j);
}
let ate = ATE_LOOP_COUNT[j - 1];
let sq = wrap_hint_squaring(skip_evaluation, all_output_hints.len(), &f_acc);
push_compare_or_return!(sq);
f_acc = sq;
t4 = wrap_chunk_point_ops_and_multiply_line_evals_step_1(
skip_evaluation,
all_output_hints.len(),
true,
None,
None,
&t4,
&p4,
None,
&p3,
t3,
None,
&p2,
t2,
None,
);
push_compare_or_return!(t4);
(t2, t3) = ((t2 + t2).into_affine(), (t3 + t3).into_affine());
let lev = wrap_chunk_point_ops_and_multiply_line_evals_step_2(
skip_evaluation,
all_output_hints.len(),
&t4,
);
push_compare_or_return!(lev);
f_acc = wrap_hints_dense_dense_mul(skip_evaluation, all_output_hints.len(), &f_acc, &lev);
push_compare_or_return!(f_acc);
if ate == 0 {
continue;
}
let c_or_cinv = if ate == -1 { c.clone() } else { gcinv.clone() };
f_acc =
wrap_hints_dense_dense_mul(skip_evaluation, all_output_hints.len(), &f_acc, &c_or_cinv);
push_compare_or_return!(f_acc);
t4 = wrap_chunk_point_ops_and_multiply_line_evals_step_1(
skip_evaluation,
all_output_hints.len(),
false,
Some(false),
Some(ate),
&t4,
&p4,
Some(gq4.to_vec()),
&p3,
t3,
Some(pubs.q3),
&p2,
t2,
Some(pubs.q2),
);
push_compare_or_return!(t4);
if ate == 1 {
(t2, t3) = ((t2 + pubs.q2).into_affine(), (t3 + pubs.q3).into_affine());
} else {
(t2, t3) = ((t2 - pubs.q2).into_affine(), (t3 - pubs.q3).into_affine());
}
let lev = wrap_chunk_point_ops_and_multiply_line_evals_step_2(
skip_evaluation,
all_output_hints.len(),
&t4,
);
push_compare_or_return!(lev);
f_acc = wrap_hints_dense_dense_mul(skip_evaluation, all_output_hints.len(), &f_acc, &lev);
push_compare_or_return!(f_acc);
}
let cp = wrap_hints_frob_fp12(skip_evaluation, all_output_hints.len(), &gcinv, 1);
push_compare_or_return!(cp);
let cp2 = wrap_hints_frob_fp12(skip_evaluation, all_output_hints.len(), &c, 2);
push_compare_or_return!(cp2);
let cp3 = wrap_hints_frob_fp12(skip_evaluation, all_output_hints.len(), &gcinv, 3);
push_compare_or_return!(cp3);
f_acc = wrap_hints_dense_dense_mul(skip_evaluation, all_output_hints.len(), &f_acc, &cp);
push_compare_or_return!(f_acc);
f_acc = wrap_hints_dense_dense_mul(skip_evaluation, all_output_hints.len(), &f_acc, &cp2);
push_compare_or_return!(f_acc);
f_acc = wrap_hints_dense_dense_mul(skip_evaluation, all_output_hints.len(), &f_acc, &cp3);
push_compare_or_return!(f_acc);
t4 = wrap_chunk_point_ops_and_multiply_line_evals_step_1(
skip_evaluation,
all_output_hints.len(),
false,
Some(true),
Some(1),
&t4,
&p4,
Some(gq4.to_vec()),
&p3,
t3,
Some(pubs.q3),
&p2,
t2,
Some(pubs.q2),
);
push_compare_or_return!(t4);
let tmp_q2f = frob_q_power(pubs.q2, 1);
t2 = (t2 + tmp_q2f).into_affine();
let tmp_q3f = frob_q_power(pubs.q3, 1);
t3 = (t3 + tmp_q3f).into_affine();
let lev = wrap_chunk_point_ops_and_multiply_line_evals_step_2(
skip_evaluation,
all_output_hints.len(),
&t4,
);
push_compare_or_return!(lev);
f_acc = wrap_hints_dense_dense_mul(skip_evaluation, all_output_hints.len(), &f_acc, &lev);
push_compare_or_return!(f_acc);
t4 = wrap_chunk_point_ops_and_multiply_line_evals_step_1(
skip_evaluation,
all_output_hints.len(),
false,
Some(true),
Some(-1),
&t4,
&p4,
Some(gq4.to_vec()),
&p3,
t3,
Some(pubs.q3),
&p2,
t2,
Some(pubs.q2),
);
push_compare_or_return!(t4);
let lev = wrap_chunk_point_ops_and_multiply_line_evals_step_2(
skip_evaluation,
all_output_hints.len(),
&t4,
);
push_compare_or_return!(lev);
f_acc = wrap_hints_dense_dense_mul(skip_evaluation, all_output_hints.len(), &f_acc, &lev);
push_compare_or_return!(f_acc);
let valid_facc = wrap_chunk_final_verify(
skip_evaluation,
all_output_hints.len(),
&f_acc,
&t4,
gq4.to_vec(),
pubs.fixed_acc,
);
push_compare_or_return!(valid_facc);
let is_valid: ark_ff::BigInt<4> = valid_facc.result.0.try_into().unwrap();
is_valid == ark_ff::BigInt::<4>::one()
}
#[allow(clippy::type_complexity)]
fn raw_input_proof_to_segments(
eval_ins: InputProofRaw,
all_output_hints: &mut Vec<Segment>,
) -> (
[Segment; 2],
[Segment; 2],
[Segment; 4],
[Segment; 6],
[Segment; NUM_PUBS],
) {
let pub_scalars: Vec<Segment> = eval_ins
.ks
.iter()
.enumerate()
.map(|(idx, f)| Segment {
id: (all_output_hints.len() + idx) as u32,
parameter_ids: vec![],
is_valid_input: true,
result: (DataType::U256Data(*f), ElementType::ScalarElem),
hints: vec![],
scr_type: ScriptType::NonDeterministic,
scr: ScriptBuf::new(),
})
.collect();
all_output_hints.extend_from_slice(&pub_scalars);
let p4vec: Vec<Segment> = [
eval_ins.p4[1],
eval_ins.p4[0],
eval_ins.p2[1],
eval_ins.p2[0],
]
.iter()
.enumerate()
.map(|(idx, f)| Segment {
id: (all_output_hints.len() + idx) as u32,
parameter_ids: vec![],
is_valid_input: true,
result: (DataType::U256Data(*f), ElementType::FieldElem),
hints: vec![],
scr_type: ScriptType::NonDeterministic,
scr: ScriptBuf::new(),
})
.collect();
all_output_hints.extend_from_slice(&p4vec);
let (gp4y, gp4x, gp2y, gp2x) = (&p4vec[0], &p4vec[1], &p4vec[2], &p4vec[3]);
let gc: Vec<Segment> = eval_ins
.c
.iter()
.enumerate()
.map(|(idx, f)| Segment {
id: (all_output_hints.len() + idx) as u32,
parameter_ids: vec![],
is_valid_input: true,
result: (DataType::U256Data(*f), ElementType::FieldElem),
hints: vec![],
scr_type: ScriptType::NonDeterministic,
scr: ScriptBuf::new(),
})
.collect();
all_output_hints.extend_from_slice(&gc);
let temp_q4: Vec<Segment> = [
eval_ins.q4[0],
eval_ins.q4[1],
eval_ins.q4[2],
eval_ins.q4[3],
]
.iter()
.enumerate()
.map(|(idx, f)| Segment {
id: (all_output_hints.len() + idx) as u32,
parameter_ids: vec![],
is_valid_input: true,
result: (DataType::U256Data(*f), ElementType::FieldElem),
hints: vec![],
scr_type: ScriptType::NonDeterministic,
scr: ScriptBuf::new(),
})
.collect();
all_output_hints.extend_from_slice(&temp_q4);
(
[gp2x.clone(), gp2y.clone()],
[gp4x.clone(), gp4y.clone()],
temp_q4.try_into().unwrap(),
gc.try_into().unwrap(),
pub_scalars.try_into().unwrap(),
)
}
#[cfg(test)]
mod test {
use crate::bn254::ell_coeffs::AffinePairing;
use ark_bn254::Bn254;
use ark_ec::{bn::BnConfig, AffineRepr, CurveGroup};
use ark_ff::{AdditiveGroup, Field};
use ark_serialize::CanonicalDeserialize;
use bitcoin_script::script;
use num_bigint::BigUint;
use std::{ops::Neg, str::FromStr};
use crate::{
bn254::ell_coeffs::BnAffinePairing,
chunk::{
api::NUM_PUBS,
taps_point_ops::{chunk_point_ops_and_multiply_line_evals_step_1, frob_q_power},
},
groth16::offchain_checker::compute_c_wi,
};
use super::{groth16_generate_segments, InputProof, PublicParams, Segment};
#[test]
fn test_groth16() {
let vk_bytes = [
115, 158, 251, 51, 106, 255, 102, 248, 22, 171, 229, 158, 80, 192, 240, 217, 99, 162,
65, 107, 31, 137, 197, 79, 11, 210, 74, 65, 65, 203, 243, 14, 123, 2, 229, 125, 198,
247, 76, 241, 176, 116, 6, 3, 241, 1, 134, 195, 39, 5, 124, 47, 31, 43, 164, 48, 120,
207, 150, 125, 108, 100, 48, 155, 137, 132, 16, 193, 139, 74, 179, 131, 42, 119, 25,
185, 98, 13, 235, 118, 92, 11, 154, 142, 134, 220, 191, 220, 169, 250, 244, 104, 123,
7, 247, 33, 178, 155, 121, 59, 75, 188, 206, 198, 182, 97, 0, 64, 231, 45, 55, 92, 100,
17, 56, 159, 79, 13, 219, 221, 33, 39, 193, 24, 36, 58, 105, 8, 70, 206, 176, 209, 146,
45, 201, 157, 226, 84, 213, 135, 143, 178, 156, 112, 137, 246, 123, 248, 215, 168, 51,
95, 177, 47, 57, 29, 199, 224, 98, 48, 144, 253, 15, 201, 192, 142, 62, 143, 13, 228,
89, 51, 58, 6, 226, 139, 99, 207, 22, 113, 215, 79, 91, 158, 166, 210, 28, 90, 218,
111, 151, 4, 55, 230, 76, 90, 209, 149, 113, 248, 245, 50, 231, 137, 51, 157, 40, 29,
184, 198, 201, 108, 199, 89, 67, 136, 239, 96, 216, 237, 172, 29, 84, 3, 128, 240, 2,
218, 169, 217, 118, 179, 34, 226, 19, 227, 59, 193, 131, 108, 20, 113, 46, 170, 196,
156, 45, 39, 151, 218, 22, 132, 250, 209, 183, 46, 249, 115, 239, 14, 176, 200, 134,
158, 148, 139, 212, 167, 152, 205, 183, 236, 242, 176, 96, 177, 187, 184, 252, 14, 226,
127, 127, 173, 147, 224, 220, 8, 29, 63, 73, 215, 92, 161, 110, 20, 154, 131, 23, 217,
116, 145, 196, 19, 167, 84, 185, 16, 89, 175, 180, 110, 116, 57, 198, 237, 147, 183,
164, 169, 220, 172, 52, 68, 175, 113, 244, 62, 104, 134, 215, 99, 132, 199, 139, 172,
108, 143, 25, 238, 201, 128, 85, 24, 73, 30, 186, 142, 186, 201, 79, 3, 176, 185, 70,
66, 89, 127, 188, 158, 209, 83, 17, 22, 187, 153, 8, 63, 58, 174, 236, 132, 226, 43,
145, 97, 242, 198, 117, 105, 161, 21, 241, 23, 84, 32, 62, 155, 245, 172, 30, 78, 41,
199, 219, 180, 149, 193, 163, 131, 237, 240, 46, 183, 186, 42, 201, 49, 249, 142, 188,
59, 212, 26, 253, 23, 27, 205, 231, 163, 76, 179, 135, 193, 152, 110, 91, 5, 218, 67,
204, 164, 128, 183, 221, 82, 16, 72, 249, 111, 118, 182, 24, 249, 91, 215, 215, 155, 2,
0, 0, 0, 0, 0, 0, 0, 212, 110, 6, 228, 73, 146, 46, 184, 158, 58, 94, 4, 141, 241, 158,
0, 175, 140, 72, 75, 52, 6, 72, 49, 112, 215, 21, 243, 151, 67, 106, 22, 158, 237, 80,
204, 41, 128, 69, 52, 154, 189, 124, 203, 35, 107, 132, 241, 234, 31, 3, 165, 87, 58,
10, 92, 252, 227, 214, 99, 176, 66, 118, 22, 177, 20, 120, 198, 252, 236, 7, 148, 207,
78, 152, 132, 94, 207, 50, 243, 4, 169, 146, 240, 79, 98, 0, 212, 106, 137, 36, 193,
21, 175, 180, 1, 26, 107, 39, 198, 89, 152, 26, 220, 138, 105, 243, 45, 63, 106, 163,
80, 74, 253, 176, 207, 47, 52, 7, 84, 59, 151, 47, 178, 165, 112, 251, 161,
]
.to_vec();
let proof_bytes: Vec<u8> = [
162, 50, 57, 98, 3, 171, 250, 108, 49, 206, 73, 126, 25, 35, 178, 148, 35, 219, 98, 90,
122, 177, 16, 91, 233, 215, 222, 12, 72, 184, 53, 2, 62, 166, 50, 68, 98, 171, 218,
218, 151, 177, 133, 223, 129, 53, 114, 236, 181, 215, 223, 91, 102, 225, 52, 122, 122,
206, 36, 122, 213, 38, 186, 170, 235, 210, 179, 221, 122, 37, 74, 38, 79, 0, 26, 94,
59, 146, 46, 252, 70, 153, 236, 126, 194, 169, 17, 144, 100, 218, 118, 22, 99, 226,
132, 40, 24, 248, 232, 197, 195, 220, 254, 52, 36, 248, 18, 167, 167, 206, 108, 29,
120, 188, 18, 78, 86, 8, 121, 217, 144, 185, 122, 58, 12, 34, 44, 6, 233, 80, 177, 183,
5, 8, 150, 74, 241, 141, 65, 150, 35, 98, 15, 150, 137, 254, 132, 167, 228, 104, 63,
133, 11, 209, 39, 79, 138, 185, 88, 20, 242, 102, 69, 73, 243, 88, 29, 91, 127, 157,
82, 192, 52, 95, 143, 49, 227, 83, 19, 26, 108, 63, 232, 213, 169, 64, 221, 159, 214,
220, 246, 174, 35, 43, 143, 80, 168, 142, 29, 103, 179, 58, 235, 33, 163, 198, 255,
188, 20, 3, 91, 47, 158, 122, 226, 201, 175, 138, 18, 24, 178, 219, 78, 12, 96, 10, 2,
133, 35, 230, 149, 235, 206, 1, 177, 211, 245, 168, 74, 62, 25, 115, 70, 42, 38, 131,
92, 103, 103, 176, 212, 223, 177, 242, 94, 14,
]
.to_vec();
let scalar = [
232, 255, 255, 239, 147, 245, 225, 67, 145, 112, 185, 121, 72, 232, 51, 40, 93, 88,
129, 129, 182, 69, 80, 184, 41, 160, 49, 225, 114, 78, 100, 48,
]
.to_vec();
let proof: ark_groth16::Proof<Bn254> =
ark_groth16::Proof::deserialize_uncompressed(&proof_bytes[..]).unwrap();
let vk: ark_groth16::VerifyingKey<Bn254> =
ark_groth16::VerifyingKey::deserialize_uncompressed(&vk_bytes[..]).unwrap();
let scalar: ark_bn254::Fr = ark_bn254::Fr::deserialize_uncompressed(&scalar[..]).unwrap();
let scalars = [scalar];
let mut msm_scalar = scalars.to_vec();
msm_scalar.reverse();
let mut msm_gs = vk.gamma_abc_g1.clone(); // vk.vk_pubs[0]
msm_gs.reverse();
let vky0 = msm_gs.pop().unwrap();
let mut pp3 = vky0 * ark_bn254::Fr::ONE;
for i in 0..NUM_PUBS {
pp3 += msm_gs[i] * msm_scalar[i];
}
let p3 = pp3.into_affine();
let (p2, p1, p4) = (proof.c, vk.alpha_g1, proof.a);
let (q3, q2, q1, q4) = (
vk.gamma_g2.into_group().neg().into_affine(),
vk.delta_g2.into_group().neg().into_affine(),
-vk.beta_g2,
proof.b,
);
let pairing = BnAffinePairing;
let f_fixed = pairing.multi_miller_loop_affine([p1], [q1]).0;
let f = pairing
.multi_miller_loop_affine([p1, p2, p3, p4], [q1, q2, q3, q4])
.0;
let (c, _s) = compute_c_wi(f);
let eval_ins: InputProof = InputProof {
p2,
p4,
q4,
c: c.c1 / c.c0,
ks: msm_scalar.clone(),
};
let eval_ins_raw = eval_ins.to_raw();
let pubs: PublicParams = PublicParams {
q2,
q3,
fixed_acc: f_fixed.c1 / f_fixed.c0,
ks_vks: msm_gs,
vky0,
};
let mut segments: Vec<Segment> = vec![];
let pass = groth16_generate_segments(false, &mut segments, eval_ins_raw, pubs, &mut None);
assert!(pass);
// hint_to_data(segments.clone());
}
// rust version of pairing verification check with normalized (1 + a. J) representation
fn verify_pairing(
ps: Vec<ark_bn254::G1Affine>,
qs: Vec<ark_bn254::G2Affine>,
gc: ark_bn254::Fq12,
_s: ark_bn254::Fq12,
p1q1: ark_bn254::Fq6,
) {
let mut cinv = gc.inverse().unwrap();
cinv = ark_bn254::Fq12::new(ark_bn254::Fq6::ONE, cinv.c1 / cinv.c0);
let mut c = gc;
c = ark_bn254::Fq12::new(ark_bn254::Fq6::ONE, c.c1 / c.c0);
let mut f = cinv;
let mut ts = qs.clone();
let ps: Vec<ark_bn254::G1Affine> = ps
.iter()
.map(|p1| ark_bn254::G1Affine::new_unchecked(-p1.x / p1.y, p1.y.inverse().unwrap()))
.collect();
let num_pairings = ps.len();
for itr in (1..ark_bn254::Config::ATE_LOOP_COUNT.len()).rev() {
let ate_bit = ark_bn254::Config::ATE_LOOP_COUNT[itr - 1];
// square
f = f * f;
f = ark_bn254::Fq12::new(ark_bn254::Fq6::ONE, f.c1 / f.c0);
// double and eval
for i in 0..num_pairings {
let t = ts[i];
let p = ps[i];
let alpha = (t.x.square() + t.x.square() + t.x.square()) / (t.y + t.y);
let neg_bias = alpha * t.x - t.y;
let mut le0 = alpha;
le0.mul_assign_by_fp(&p.x);
let mut le1 = neg_bias;
le1.mul_assign_by_fp(&p.y);
let mut le = ark_bn254::Fq12::ZERO;
le.c0.c0 = ark_bn254::fq2::Fq2::ONE;
le.c1.c0 = le0;
le.c1.c1 = le1;
f *= le;
f = ark_bn254::Fq12::new(ark_bn254::Fq6::ONE, f.c1 / f.c0);
ts[i] = (t + t).into_affine();
}
if ate_bit == 1 || ate_bit == -1 {
let c_or_cinv = if ate_bit == -1 { c } else { cinv };
f *= c_or_cinv;
f = ark_bn254::Fq12::new(ark_bn254::Fq6::ONE, f.c1 / f.c0);
for i in 0..num_pairings {
let t = ts[i];
let mut q = qs[i];
let p = ps[i];
if ate_bit == -1 {
q = q.neg();
};
let alpha = (t.y - q.y) / (t.x - q.x);
let neg_bias = alpha * t.x - t.y;
let mut le0 = alpha;
le0.mul_assign_by_fp(&p.x);
let mut le1 = neg_bias;
le1.mul_assign_by_fp(&p.y);
let mut le = ark_bn254::Fq12::ZERO;
le.c0.c0 = ark_bn254::fq2::Fq2::ONE;
le.c1.c0 = le0;
le.c1.c1 = le1;
f *= le;
f = ark_bn254::Fq12::new(ark_bn254::Fq6::ONE, f.c1 / f.c0);
ts[i] = (t + q).into_affine();
}
}
}
let cinv_q = cinv.frobenius_map(1);
let c_q2 = c.frobenius_map(2);
let cinv_q3 = cinv.frobenius_map(3);
for mut cq in vec![cinv_q, c_q2, cinv_q3] {
cq = ark_bn254::Fq12::new(ark_bn254::Fq6::ONE, cq.c1 / cq.c0);
f *= cq;
f = ark_bn254::Fq12::new(ark_bn254::Fq6::ONE, f.c1 / f.c0);
}
for i in 0..num_pairings {
let mut q = qs[i];
let t = ts[i];
let p = ps[i];
q = frob_q_power(q, 1);
let alpha = (t.y - q.y) / (t.x - q.x);
let neg_bias = alpha * t.x - t.y;
let mut le0 = alpha;
le0.mul_assign_by_fp(&p.x);
let mut le1 = neg_bias;
le1.mul_assign_by_fp(&p.y);
let mut le = ark_bn254::Fq12::ZERO;
le.c0.c0 = ark_bn254::fq2::Fq2::ONE;
le.c1.c0 = le0;
le.c1.c1 = le1;
f *= le;
f = ark_bn254::Fq12::new(ark_bn254::Fq6::ONE, f.c1 / f.c0);
ts[i] = (t + q).into_affine();
}
// t + q^3
for i in 0..num_pairings {
let mut q = qs[i];
let t = ts[i];
let p = ps[i];
q = frob_q_power(q, -1);
let alpha = (t.y - q.y) / (t.x - q.x);
let neg_bias = alpha * t.x - t.y;
let mut le0 = alpha;
le0.mul_assign_by_fp(&p.x);
let mut le1 = neg_bias;
le1.mul_assign_by_fp(&p.y);
let mut le = ark_bn254::Fq12::ZERO;
le.c0.c0 = ark_bn254::fq2::Fq2::ONE;
le.c1.c0 = le0;
le.c1.c1 = le1;
f *= le;
f = ark_bn254::Fq12::new(ark_bn254::Fq6::ONE, f.c1 / f.c0);
ts[i] = (t + q).into_affine();
}
// t + q^3
for i in 0..num_pairings {
let mut q = qs[i];
let t = ts[i];
q = frob_q_power(q, 3);
ts[i] = (t + q).into_affine();
}
assert_eq!(f.c1 + p1q1, ark_bn254::Fq6::ZERO); // final check, f: (a+b == 0 => (1 + a) * (1 + b) == Fq12::ONE)
}
// Pairing verification check with normalized (1 + a. J) representation
// Includes equivalent bitcoin script in for each functions
pub fn verify_pairing_scripted(
ps: Vec<ark_bn254::G1Affine>,
qs: Vec<ark_bn254::G2Affine>,
gc: ark_bn254::Fq12,
_s: ark_bn254::Fq12,
p1q1: ark_bn254::Fq6,
) {
use crate::chunk::{
taps_ext_miller::chunk_frob_fp12,
taps_mul::{chunk_dense_dense_mul, chunk_fq12_square},
taps_point_ops::{
chunk_init_t4, chunk_point_ops_and_multiply_line_evals_step_2, frob_q_power,
},
};
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 mut cinv = gc.inverse().unwrap();
cinv = ark_bn254::Fq12::new(ark_bn254::Fq6::ONE, cinv.c1 / cinv.c0);
let mut c = gc;
c = ark_bn254::Fq12::new(ark_bn254::Fq6::ONE, c.c1 / c.c0);
let mut f = cinv;
let mut g = cinv.c1;
let mut ts = qs.clone();
let ps: Vec<ark_bn254::G1Affine> = ps
.iter()
.map(|p1| ark_bn254::G1Affine::new_unchecked(-p1.x / p1.y, p1.y.inverse().unwrap()))
.collect();
let num_pairings = ps.len();
let mut total_script_size = 0;
#[allow(unused_assignments)] // clippy bug?
let mut temp_scr = script! {};
let (mut t4, _, scr, _) = chunk_init_t4([
qs[2].x.c0.into(),
qs[2].x.c1.into(),
qs[2].y.c0.into(),
qs[2].y.c1.into(),
]);
total_script_size += scr.len();
let mut t3 = qs[1];
let mut t2 = qs[0];
for itr in (1..ark_bn254::Config::ATE_LOOP_COUNT.len()).rev() {
let ate_bit = ark_bn254::Config::ATE_LOOP_COUNT[itr - 1];
println!("itr {} ate_bit {}", itr, ate_bit);
// square
f = f * f;
f = ark_bn254::Fq12::new(ark_bn254::Fq6::ONE, f.c1 / f.c0);
(g, _, temp_scr, _) = chunk_fq12_square(g);
total_script_size += temp_scr.len();
assert_eq!(g, f.c1);
// double and eval
for i in 0..num_pairings {
let t = ts[i];
let p = ps[i];
let alpha = (t.x.square() + t.x.square() + t.x.square()) / (t.y + t.y);
let neg_bias = alpha * t.x - t.y;
let mut le0 = alpha;
le0.mul_assign_by_fp(&p.x);
let mut le1 = neg_bias;
le1.mul_assign_by_fp(&p.y);
let mut le = ark_bn254::Fq12::ZERO;
le.c0.c0 = ark_bn254::fq2::Fq2::ONE;
le.c1.c0 = le0;
le.c1.c1 = le1;
f *= le;
f = ark_bn254::Fq12::new(ark_bn254::Fq6::ONE, f.c1 / f.c0);
ts[i] = (t + t).into_affine();
}
(t4, _, temp_scr, _) = chunk_point_ops_and_multiply_line_evals_step_1(
true, None, None, t4, ps[2], None, ps[1], t3, None, ps[0], t2, None,
);
total_script_size += temp_scr.len();
t3 = (t3 + t3).into_affine();
t2 = (t2 + t2).into_affine();
let (lev, _, scr, _) = chunk_point_ops_and_multiply_line_evals_step_2(t4);
total_script_size += scr.len();
(g, _, temp_scr, _) = chunk_dense_dense_mul(g, lev);
total_script_size += temp_scr.len();
assert_eq!(g, f.c1);
if ate_bit == 1 || ate_bit == -1 {
let c_or_cinv = if ate_bit == -1 { c } else { cinv };
f *= c_or_cinv;
f = ark_bn254::Fq12::new(ark_bn254::Fq6::ONE, f.c1 / f.c0);
(g, _, temp_scr, _) = chunk_dense_dense_mul(g, c_or_cinv.c1);
total_script_size += temp_scr.len();
assert_eq!(g, f.c1);
for i in 0..num_pairings {
let t = ts[i];
let mut q = qs[i];
let p = ps[i];
if ate_bit == -1 {
q = q.neg();
};
let alpha = (t.y - q.y) / (t.x - q.x);
let neg_bias = alpha * t.x - t.y;
let mut le0 = alpha;
le0.mul_assign_by_fp(&p.x);
let mut le1 = neg_bias;
le1.mul_assign_by_fp(&p.y);
let mut le = ark_bn254::Fq12::ZERO;
le.c0.c0 = ark_bn254::fq2::Fq2::ONE;
le.c1.c0 = le0;
le.c1.c1 = le1;
f *= le;
f = ark_bn254::Fq12::new(ark_bn254::Fq6::ONE, f.c1 / f.c0);
ts[i] = (t + q).into_affine();
// println!("pair {:?} ts {:?}", i, ts[i]);
}
(t4, _, temp_scr, _) = chunk_point_ops_and_multiply_line_evals_step_1(
false,
Some(false),
Some(ate_bit),
t4,
ps[2],
Some(qs[2]),
ps[1],
t3,
Some(qs[1]),
ps[0],
t2,
Some(qs[0]),
);
total_script_size += temp_scr.len();
if ate_bit == 1 {
t3 = (t3 + qs[1]).into_affine();
t2 = (t2 + qs[0]).into_affine();
} else {
t3 = (t3 + qs[1].neg()).into_affine();
t2 = (t2 + qs[0].neg()).into_affine();
}
let (lev, _, scr, _) = chunk_point_ops_and_multiply_line_evals_step_2(t4);
total_script_size += scr.len();
(g, _, temp_scr, _) = chunk_dense_dense_mul(g, lev);
total_script_size += temp_scr.len();
}
assert_eq!(g, f.c1);
}
let cinv_q = cinv.frobenius_map(1);
let c_q2 = c.frobenius_map(2);
let cinv_q3 = cinv.frobenius_map(3);
let (sc_cinv_q, _, scr, _) = chunk_frob_fp12(cinv.c1, 1);
total_script_size += scr.len();
let (sc_c_q2, _, scr, _) = chunk_frob_fp12(c.c1, 2);
total_script_size += scr.len();
let (sc_cinv_q3, _, scr, _) = chunk_frob_fp12(cinv.c1, 3);
total_script_size += scr.len();
for mut cq in vec![cinv_q, c_q2, cinv_q3] {
cq = ark_bn254::Fq12::new(ark_bn254::Fq6::ONE, cq.c1 / cq.c0);
f *= cq;
f = ark_bn254::Fq12::new(ark_bn254::Fq6::ONE, f.c1 / f.c0);
}
for sc_cq in vec![sc_cinv_q, sc_c_q2, sc_cinv_q3] {
(g, _, temp_scr, _) = chunk_dense_dense_mul(g, sc_cq);
total_script_size += temp_scr.len();
}
assert_eq!(g, f.c1);
for i in 0..num_pairings {
let mut q = qs[i];
let t = ts[i];
let p = ps[i];
q.x.conjugate_in_place();
q.x *= beta_12;
q.y.conjugate_in_place();
q.y *= beta_13;
let alpha = (t.y - q.y) / (t.x - q.x);
let neg_bias = alpha * t.x - t.y;
let mut le0 = alpha;
le0.mul_assign_by_fp(&p.x);
let mut le1 = neg_bias;
le1.mul_assign_by_fp(&p.y);
let mut le = ark_bn254::Fq12::ZERO;
le.c0.c0 = ark_bn254::fq2::Fq2::ONE;
le.c1.c0 = le0;
le.c1.c1 = le1;
f *= le;
f = ark_bn254::Fq12::new(ark_bn254::Fq6::ONE, f.c1 / f.c0);
ts[i] = (t + q).into_affine();
}
(t4, _, temp_scr, _) = chunk_point_ops_and_multiply_line_evals_step_1(
false,
Some(true),
Some(1),
t4,
ps[2],
Some(qs[2]),
ps[1],
t3,
Some(qs[1]),
ps[0],
t2,
Some(qs[0]),
);
total_script_size += temp_scr.len();
let (lev, _, scr, _) = chunk_point_ops_and_multiply_line_evals_step_2(t4);
total_script_size += scr.len();
(g, _, temp_scr, _) = chunk_dense_dense_mul(g, lev);
total_script_size += temp_scr.len();
let tmp_q2f = frob_q_power(qs[0], 1);
t2 = (t2 + tmp_q2f).into_affine();
let tmp_q3f = frob_q_power(qs[1], 1);
t3 = (t3 + tmp_q3f).into_affine();
assert_eq!(g, f.c1);