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alt_bn128_pair.cairo
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alt_bn128_pair.cairo
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from bigint import BigInt3, nondet_bigint3, bigint_mul, UnreducedBigInt5
from alt_bn128_def import P0, P1, P2
from alt_bn128_field import (
is_zero,
FQ12,
verify_zero5,
fq12_is_zero,
nondet_fq12,
fq12_one,
fq12_diff,
fq12_pow_12,
fq12_pow_3,
fq12_zero,
)
from alt_bn128_g1 import G1Point, compute_doubling_slope, compute_slope
from alt_bn128_g2 import G2Point
from alt_bn128_gt import (
GTPoint,
gt_slope,
gt_doubling_slope,
twist,
g1_to_gt,
fq12_mul,
gt_double,
gt_add,
)
const ate_loop_count = 29793968203157093288;
const log_ate_loop_count = 63;
from starkware.cairo.common.registers import get_label_location
func get_loop_count_bits(index: felt) -> (bits: felt) {
let (data) = get_label_location(bits);
let bit_array = cast(data, felt*);
return (bit_array[index],);
bits:
dw 0;
dw 0;
dw 0;
dw 1;
dw 0;
dw 1;
dw 0;
dw 1;
dw 1;
dw 1;
dw 0;
dw 1;
dw 1;
dw 1;
dw 0;
dw 0;
dw 0;
dw 1;
dw 1;
dw 0;
dw 1;
dw 1;
dw 1;
dw 0;
dw 0;
dw 1;
dw 1;
dw 1;
dw 1;
dw 1;
dw 0;
dw 1;
dw 1;
dw 0;
dw 0;
dw 1;
dw 1;
dw 1;
dw 0;
dw 0;
dw 0;
dw 0;
dw 0;
dw 0;
dw 1;
dw 1;
dw 1;
dw 0;
dw 1;
dw 0;
dw 0;
dw 1;
dw 1;
dw 1;
dw 1;
dw 0;
dw 1;
dw 0;
dw 1;
dw 1;
dw 1;
dw 0;
dw 0;
dw 1;
}
func gt_linehelp{range_check_ptr}(pt0: GTPoint, pt1: GTPoint, t: GTPoint, slope: FQ12) -> (
res: FQ12
) {
%{
import sys, os
cwd = os.getcwd()
sys.path.append(cwd)
from utils.bn128_field import FQ, FQ12
from utils.bn128_utils import parse_fq12
x1 = FQ12(list(map(FQ, parse_fq12(ids.pt1.x))))
y1 = FQ12(list(map(FQ, parse_fq12(ids.pt1.y))))
xt = FQ12(list(map(FQ, parse_fq12(ids.t.x))))
yt = FQ12(list(map(FQ, parse_fq12(ids.t.y))))
res = (slope * (xt - x1) - (yt - y1))
value = list(map(lambda x: x.n, res.coeffs))
%}
let (res: FQ12) = nondet_fq12();
// TODO VERIFY
// let (x_diff_slope : UnreducedBigInt5) = bigint_mul(
// BigInt3(d0=t.x.d0 - pt1.x.d0, d1=t.x.d1 - pt1.x.d1, d2=t.x.d2 - pt1.x.d2), slope)
// verify_zero5(
// UnreducedBigInt5(
// d0=x_diff_slope.d0 - t.y.d0 + pt0.x.d0 - res.d0,
// d1=x_diff_slope.d1 - t.y.d1 + pt0.x.d1 - res.d1,
// d2=x_diff_slope.d2 - t.y.d2 + pt0.x.d2 - res.d2,
// d3=x_diff_slope.d3,
// d4=x_diff_slope.d4))
return (res,);
}
func gt_linefunc{range_check_ptr}(pt0: GTPoint, pt1: GTPoint, t: GTPoint) -> (res: FQ12) {
let (x_diff: FQ12) = fq12_diff(pt0.x, pt1.x);
let (same_x: felt) = fq12_is_zero(x_diff);
if (same_x == 0) {
let (slope: FQ12) = gt_slope(pt0, pt1);
let (res: FQ12) = gt_linehelp(pt0, pt1, t, slope);
return (res=res);
} else {
let (y_diff: FQ12) = fq12_diff(pt0.y, pt1.y);
let (same_y: felt) = fq12_is_zero(y_diff);
if (same_y == 1) {
let (slope: FQ12) = gt_doubling_slope(pt0);
let (res: FQ12) = gt_linehelp(pt0, pt1, t, slope);
return (res=res);
} else {
let (res: FQ12) = fq12_diff(t.x, pt0.x);
return (res=res);
}
}
}
func miller_loop{range_check_ptr}(Q: GTPoint, P: GTPoint, R: GTPoint, n: felt, f: FQ12) -> (
res: FQ12
) {
// END OF LOOP
if (n == 0) {
alloc_locals;
let modulus = BigInt3(P0, P1, P2);
let (_, local q1x) = fq12_pow_3(Q.x, modulus);
let (_, local q1y) = fq12_pow_3(Q.y, modulus);
let Q1 = GTPoint(q1x, q1y);
let (local lfRQ1P: FQ12) = gt_linefunc(R, Q1, P);
let (local newR: GTPoint) = gt_add(R, Q1);
let (_, local nq2x) = fq12_pow_3(q1x, modulus);
let (_, local q2y) = fq12_pow_3(q1y, modulus);
let (zero) = fq12_zero();
let (nq2y) = fq12_diff(zero, q2y);
let nQ2 = GTPoint(nq2x, nq2y);
let (local lfnQ2P: FQ12) = gt_linefunc(newR, nQ2, P);
let (local f_1: FQ12) = fq12_mul(f, lfRQ1P);
let (f_2: FQ12) = fq12_mul(f_1, lfnQ2P);
// final exponentiation
return final_exponentiation(f_2);
}
alloc_locals;
// inner loop
let (bit) = get_loop_count_bits(n - 1);
let (local f_sqr: FQ12) = fq12_mul(f, f);
let (local lfRRP: FQ12) = gt_linefunc(R, R, P);
let (local f_sqr_l: FQ12) = fq12_mul(f_sqr, lfRRP);
let (twoR: GTPoint) = gt_double(R);
if (bit == 0) {
return miller_loop(Q=Q, P=P, R=twoR, n=n - 1, f=f_sqr_l);
} else {
let (local lfRQP: FQ12) = gt_linefunc(twoR, Q, P);
let (local new_f: FQ12) = fq12_mul(f_sqr_l, lfRQP);
let (twoRpQ: GTPoint) = gt_add(twoR, Q);
return miller_loop(Q=Q, P=P, R=twoRpQ, n=n - 1, f=new_f);
}
}
func pairing{range_check_ptr}(Q: G2Point, P: G1Point) -> (res: FQ12) {
alloc_locals;
let (local twisted_Q: GTPoint) = twist(Q);
let (local f: FQ12) = fq12_one();
let (cast_P: GTPoint) = g1_to_gt(P);
return miller_loop(Q=twisted_Q, P=cast_P, R=twisted_Q, n=log_ate_loop_count + 1, f=f);
}
func final_exponentiation{range_check_ptr}(x: FQ12) -> (res: FQ12) {
let final_exponent = FQ12(
BigInt3(d0=6212946889023415678071072, d1=45799200417935711304343445, d2=42770771512020533619734522),
BigInt3(d0=59170517635015779814843574, d1=69861904660805168774244518, d2=18175251611003261941144987),
BigInt3(d0=6224840365716485556659866, d1=72079669560153613533475076, d2=54097091982365706908871098),
BigInt3(d0=23778027891331508348714600, d1=27070990064893031605816996, d2=66880530963181666257122137),
BigInt3(d0=6428453163241839293638384, d1=3915066362894641347128887, d2=57669624004488276782181297),
BigInt3(d0=67978089800637315191356650, d1=51071509339440355656395904, d2=68120774182643646161376785),
BigInt3(d0=25088979566862161605950544, d1=63116802240563251842289738, d2=36250774203703337112865410),
BigInt3(d0=42045420448204954441533445, d1=76593899932297329118450698, d2=60079122095221526332763037),
BigInt3(d0=46087482279252059585677525, d1=41252762411239220367854994, d2=14786342199147618000549637),
BigInt3(d0=27452466885733176020010742, d1=32571718558893095687996369, d2=74875694450552131089070851),
BigInt3(d0=72489332814153009192769011, d1=9971105602881718038104912, d2=203128949104),
BigInt3(d0=0, d1=0, d2=0),
);
return fq12_pow_12(x, final_exponent);
}