openvm_pairing_guest/bls12_381/
mod.rs

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1use core::ops::Neg;
2
3use openvm_algebra_guest::{Field, IntMod};
4use openvm_algebra_moduli_macros::moduli_declare;
5use openvm_ecc_guest::{weierstrass::IntrinsicCurve, CyclicGroup, Group};
6
7mod fp12;
8mod fp2;
9mod pairing;
10#[cfg(all(feature = "halo2curves", not(target_os = "zkvm")))]
11pub(crate) mod utils;
12
13pub use fp12::*;
14pub use fp2::*;
15use hex_literal::hex;
16#[cfg(not(target_os = "zkvm"))]
17use lazy_static::lazy_static;
18#[cfg(not(target_os = "zkvm"))]
19use num_bigint::BigUint;
20use openvm_ecc_sw_macros::sw_declare;
21
22use crate::pairing::PairingIntrinsics;
23
24#[cfg(all(test, feature = "halo2curves", not(target_os = "zkvm")))]
25mod tests;
26
27#[cfg(not(target_os = "zkvm"))]
28lazy_static! {
29    pub static ref BLS12_381_MODULUS: BigUint = BigUint::from_bytes_be(&hex!(
30        "1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab"
31    ));
32    pub static ref BLS12_381_ORDER: BigUint = BigUint::from_bytes_be(&hex!(
33        "73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001"
34    ));
35}
36
37pub const BLS12_381_XI_ISIZE: [isize; 2] = [1, 1];
38pub const BLS12_381_NUM_LIMBS: usize = 48;
39pub const BLS12_381_LIMB_BITS: usize = 8;
40pub const BLS12_381_BLOCK_SIZE: usize = 16;
41
42pub const BLS12_381_SEED_ABS: u64 = 0xd201000000010000;
43// Encodes the Bls12_381 seed, x.
44// x = sum_i BLS12_381_PSEUDO_BINARY_ENCODING[i] * 2^i
45// where BLS12_381_PSEUDO_BINARY_ENCODING[i] is in {-1, 0, 1}
46// Validated against BLS12_381_SEED_ABS by a test in tests.rs
47pub const BLS12_381_PSEUDO_BINARY_ENCODING: [i8; 64] = [
48    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
49    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1,
50];
51
52moduli_declare! {
53    Bls12_381Fp { modulus = "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab" },
54    Bls12_381Scalar { modulus = "0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001" },
55}
56
57const CURVE_B: Bls12_381Fp = Bls12_381Fp::from_const_u8(4);
58
59sw_declare! {
60    Bls12_381G1Affine { mod_type = Bls12_381Fp, b = CURVE_B },
61}
62
63pub type Fp = Bls12_381Fp;
64pub type Scalar = Bls12_381Scalar;
65/// Affine point representation of `Fp` points of BLS12-381.
66/// **Note**: an instance of this type may be constructed that lies
67/// on the curve but not necessarily in the prime order subgroup
68/// because the group has cofactors.
69pub type G1Affine = Bls12_381G1Affine;
70pub use g2::G2Affine;
71
72impl Field for Fp {
73    type SelfRef<'a> = &'a Self;
74    const ZERO: Self = <Self as IntMod>::ZERO;
75    const ONE: Self = <Self as IntMod>::ONE;
76
77    fn double_assign(&mut self) {
78        IntMod::double_assign(self);
79    }
80
81    fn square_assign(&mut self) {
82        IntMod::square_assign(self);
83    }
84}
85
86impl Field for Scalar {
87    type SelfRef<'a> = &'a Self;
88    const ZERO: Self = <Self as IntMod>::ZERO;
89    const ONE: Self = <Self as IntMod>::ONE;
90
91    fn double_assign(&mut self) {
92        IntMod::double_assign(self);
93    }
94
95    fn square_assign(&mut self) {
96        IntMod::square_assign(self);
97    }
98}
99
100// https://hackmd.io/@benjaminion/bls12-381#Cofactor
101// BLS12-381: The from_xy function will allow constructing elements that lie on the curve
102// but aren't actually in the cyclic subgroup of prime order that is usually called G1.
103impl CyclicGroup for G1Affine {
104    // https://github.com/zcash/librustzcash/blob/6e0364cd42a2b3d2b958a54771ef51a8db79dd29/pairing/src/bls12_381/README.md#generators
105    const GENERATOR: Self = G1Affine {
106        x: Bls12_381Fp::from_const_bytes(hex!(
107            "BBC622DB0AF03AFBEF1A7AF93FE8556C58AC1B173F3A4EA105B974974F8C68C30FACA94F8C63952694D79731A7D3F117"
108        )),
109        y: Bls12_381Fp::from_const_bytes(hex!(
110            "E1E7C5462923AA0CE48A88A244C73CD0EDB3042CCB18DB00F60AD0D595E0F5FCE48A1D74ED309EA0F1A0AAE381F4B308"
111        )),
112    };
113    const NEG_GENERATOR: Self = G1Affine {
114        x: Bls12_381Fp::from_const_bytes(hex!(
115            "BBC622DB0AF03AFBEF1A7AF93FE8556C58AC1B173F3A4EA105B974974F8C68C30FACA94F8C63952694D79731A7D3F117"
116        )),
117        y: Bls12_381Fp::from_const_bytes(hex!(
118            "CAC239B9D6DC54AD1B75CB0EBA386F4E3642ACCAD5B95566C907B51DEF6A8167F2212ECFC8767DAAA845D555681D4D11"
119        )),
120    };
121}
122
123pub struct Bls12_381;
124
125impl IntrinsicCurve for Bls12_381 {
126    type Scalar = Scalar;
127    type Point = G1Affine;
128
129    fn msm(coeffs: &[Self::Scalar], bases: &[Self::Point]) -> Self::Point {
130        openvm_ecc_guest::msm(coeffs, bases)
131    }
132}
133
134// Define a G2Affine struct that implements curve operations using `Fp2` intrinsics
135// but not special E(Fp2) intrinsics.
136mod g2 {
137    use openvm_algebra_guest::Field;
138    use openvm_ecc_guest::{
139        impl_sw_affine, impl_sw_group_ops, weierstrass::WeierstrassPoint, AffinePoint, Group,
140    };
141
142    use super::{Fp, Fp2};
143
144    const THREE: Fp2 = Fp2::new(Fp::from_const_u8(3), Fp::ZERO);
145    const B: Fp2 = Fp2::new(Fp::from_const_u8(4), Fp::from_const_u8(4));
146    impl_sw_affine!(G2Affine, Fp2, THREE, B);
147    impl_sw_group_ops!(G2Affine, Fp2);
148}
149
150impl PairingIntrinsics for Bls12_381 {
151    type Fp = Fp;
152    type Fp2 = Fp2;
153    type Fp12 = Fp12;
154
155    const PAIRING_IDX: usize = 1;
156    // The sextic extension `Fp12` is `Fp2[X] / (X^6 - \xi)`, where `\xi` is a non-residue.
157    const XI: Fp2 = Fp2::new(Fp::from_const_u8(1), Fp::from_const_u8(1));
158    const FP2_TWO: Fp2 = Fp2::new(Fp::from_const_u8(2), Fp::from_const_u8(0));
159    const FP2_THREE: Fp2 = Fp2::new(Fp::from_const_u8(3), Fp::from_const_u8(0));
160
161    // Multiplication constants for the Frobenius map for coefficients in Fp2 c1..=c5 for powers 0..12
162    // FROBENIUS_COEFFS\[i\]\[j\] = \xi^{(j + 1) * (p^i - 1)/6} when p = 1 (mod 6)
163    // These are validated against `halo2curves::bls12_381::FROBENIUS_COEFF_FQ12_C1` in tests.rs
164    const FROBENIUS_COEFFS: [[Self::Fp2; 5]; 12] = [
165        [
166            Fp2 {
167                c0: Bls12_381Fp(hex!(
168                    "010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
169                )),
170                c1: Bls12_381Fp(hex!(
171                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
172                    ")),
173            },
174            Fp2 {
175                c0: Bls12_381Fp(hex!(
176                    "010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
177                )),
178                c1: Bls12_381Fp(hex!(
179                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
180                    ")),
181            },
182            Fp2 {
183                c0: Bls12_381Fp(hex!(
184                    "010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
185                )),
186                c1: Bls12_381Fp(hex!(
187                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
188                    ")),
189            },
190            Fp2 {
191                c0: Bls12_381Fp(hex!(
192                    "010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
193                )),
194                c1: Bls12_381Fp(hex!(
195                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
196                    ")),
197            },
198            Fp2 {
199                c0: Bls12_381Fp(hex!(
200                    "010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
201                )),
202                c1: Bls12_381Fp(hex!(
203                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
204                    ")),
205            },
206        ],
207        [
208            Fp2 {
209                c0: Bls12_381Fp(hex!(
210                    "b85f2392ed75078d3d81e7633da57ef6c4b9ba84d743247b4f5fbd3cfd03d60f1f0d2c20b4be31c26706bb02bfd30419"
211                )),
212                c1: Bls12_381Fp(hex!(
213                    "f34adc6d128af72cc27e6c4dc15a2d285f3cf671c98e0cec6fb3c7b68747a154b89f1f2302e9e98832e0c4362b3efc00"
214                ))
215            },
216            Fp2 {
217                c0: Bls12_381Fp(hex!(
218                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
219                )),
220                c1: Bls12_381Fp(hex!(
221                    "acaa00000000fd8bfdff494feb2794409b5fb80f65297d89d49a75897d850daa85ded463864002ec99e67f39ea11011a"
222                ))
223            },
224            Fp2 {
225                c0: Bls12_381Fp(hex!(
226                    "09cce3edfb8410c8f405ec722f9967eec5419200176ef7775e43d3c2ab5d3948fe7fd16b6de331680b40ff37040eaf06"
227                )),
228                c1: Bls12_381Fp(hex!(
229                    "09cce3edfb8410c8f405ec722f9967eec5419200176ef7775e43d3c2ab5d3948fe7fd16b6de331680b40ff37040eaf06"
230                ))
231            },
232            Fp2 {
233                c0: Bls12_381Fp(hex!(
234                    "adaa00000000fd8bfdff494feb2794409b5fb80f65297d89d49a75897d850daa85ded463864002ec99e67f39ea11011a"
235                )),
236                c1: Bls12_381Fp(hex!(
237                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
238                ))
239            },
240            Fp2 {
241                c0: Bls12_381Fp(hex!(
242                    "16810780e9fa189b32877f256e3e3ac666059c8e4ddfea8bee8f0b0c241698f345e0b1486bfa47dfd85f3a01d9cfb205"
243                )),
244                c1: Bls12_381Fp(hex!(
245                    "9529f87f1605e61ecd78d48b90c17158bdf0146853f345dbd08279e76035df7091cc99fa4aadd36bc186453811424e14"
246                ))
247            },
248        ],
249        [
250            Fp2 {
251                c0: Bls12_381Fp(hex!(
252                    "fffffeffffff012e02000a6213d817de8896f8e63ba9b3ddea770f6a07c669ba51ce76df2f67195f0000000000000000"
253                )),
254                c1: Bls12_381Fp(hex!(
255                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
256                ))
257            },
258            Fp2 {
259                c0: Bls12_381Fp(hex!(
260                    "fefffeffffff012e02000a6213d817de8896f8e63ba9b3ddea770f6a07c669ba51ce76df2f67195f0000000000000000"
261                )),
262                c1: Bls12_381Fp(hex!(
263                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
264                ))
265            },
266            Fp2 {
267                c0: Bls12_381Fp(hex!(
268                    "aaaafffffffffeb9ffff53b1feffab1e24f6b0f6a0d23067bf1285f3844b7764d7ac4b43b6a71b4b9ae67f39ea11011a"
269                )),
270                c1: Bls12_381Fp(hex!(
271                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
272                ))
273            },
274            Fp2 {
275                c0: Bls12_381Fp(hex!(
276                    "acaa00000000fd8bfdff494feb2794409b5fb80f65297d89d49a75897d850daa85ded463864002ec99e67f39ea11011a"
277                )),
278                c1: Bls12_381Fp(hex!(
279                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
280                ))
281            },
282            Fp2 {
283                c0: Bls12_381Fp(hex!(
284                    "adaa00000000fd8bfdff494feb2794409b5fb80f65297d89d49a75897d850daa85ded463864002ec99e67f39ea11011a"
285                )),
286                c1: Bls12_381Fp(hex!(
287                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
288                ))
289            },
290        ],
291        [
292            Fp2 {
293                c0: Bls12_381Fp(hex!(
294                    "a2de1b12047beef10afa673ecf6644305eb41ef6896439ef60cfb130d9ed3d1cd92c7ad748c4e9e28ea68001e6035213"
295                )),
296                c1: Bls12_381Fp(hex!(
297                    "09cce3edfb8410c8f405ec722f9967eec5419200176ef7775e43d3c2ab5d3948fe7fd16b6de331680b40ff37040eaf06"
298                ))
299            },
300            Fp2 {
301                c0: Bls12_381Fp(hex!(
302                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
303                )),
304                c1: Bls12_381Fp(hex!(
305                    "010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
306                ))
307            },
308            Fp2 {
309                c0: Bls12_381Fp(hex!(
310                    "a2de1b12047beef10afa673ecf6644305eb41ef6896439ef60cfb130d9ed3d1cd92c7ad748c4e9e28ea68001e6035213"
311                )),
312                c1: Bls12_381Fp(hex!(
313                    "a2de1b12047beef10afa673ecf6644305eb41ef6896439ef60cfb130d9ed3d1cd92c7ad748c4e9e28ea68001e6035213"
314                ))
315            },
316            Fp2 {
317                c0: Bls12_381Fp(hex!(
318                    "aaaafffffffffeb9ffff53b1feffab1e24f6b0f6a0d23067bf1285f3844b7764d7ac4b43b6a71b4b9ae67f39ea11011a"
319                )),
320                c1: Bls12_381Fp(hex!(
321                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
322                ))
323            },
324            Fp2 {
325                c0: Bls12_381Fp(hex!(
326                    "09cce3edfb8410c8f405ec722f9967eec5419200176ef7775e43d3c2ab5d3948fe7fd16b6de331680b40ff37040eaf06"
327                )),
328                c1: Bls12_381Fp(hex!(
329                    "a2de1b12047beef10afa673ecf6644305eb41ef6896439ef60cfb130d9ed3d1cd92c7ad748c4e9e28ea68001e6035213"
330                ))
331            },
332        ],
333        [
334            Fp2 {
335                c0: Bls12_381Fp(hex!(
336                    "fefffeffffff012e02000a6213d817de8896f8e63ba9b3ddea770f6a07c669ba51ce76df2f67195f0000000000000000"
337                )),
338                c1: Bls12_381Fp(hex!(
339                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
340                ))
341            },
342            Fp2 {
343                c0: Bls12_381Fp(hex!(
344                    "acaa00000000fd8bfdff494feb2794409b5fb80f65297d89d49a75897d850daa85ded463864002ec99e67f39ea11011a"
345                )),
346                c1: Bls12_381Fp(hex!(
347                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
348                ))
349            },
350            Fp2 {
351                c0: Bls12_381Fp(hex!(
352                    "010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
353                )),
354                c1: Bls12_381Fp(hex!(
355                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
356                ))
357            },
358            Fp2 {
359                c0: Bls12_381Fp(hex!(
360                    "fefffeffffff012e02000a6213d817de8896f8e63ba9b3ddea770f6a07c669ba51ce76df2f67195f0000000000000000"
361                )),
362                c1: Bls12_381Fp(hex!(
363                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
364                ))
365            },
366            Fp2 {
367                c0: Bls12_381Fp(hex!(
368                    "acaa00000000fd8bfdff494feb2794409b5fb80f65297d89d49a75897d850daa85ded463864002ec99e67f39ea11011a"
369                )),
370                c1: Bls12_381Fp(hex!(
371                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
372                ))
373            },
374        ],
375        [
376            Fp2 {
377                c0: Bls12_381Fp(hex!(
378                    "9529f87f1605e61ecd78d48b90c17158bdf0146853f345dbd08279e76035df7091cc99fa4aadd36bc186453811424e14"
379                )),
380                c1: Bls12_381Fp(hex!(
381                    "16810780e9fa189b32877f256e3e3ac666059c8e4ddfea8bee8f0b0c241698f345e0b1486bfa47dfd85f3a01d9cfb205"
382                ))
383            },
384            Fp2 {
385                c0: Bls12_381Fp(hex!(
386                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
387                )),
388                c1: Bls12_381Fp(hex!(
389                    "fefffeffffff012e02000a6213d817de8896f8e63ba9b3ddea770f6a07c669ba51ce76df2f67195f0000000000000000"
390                ))
391            },
392            Fp2 {
393                c0: Bls12_381Fp(hex!(
394                    "09cce3edfb8410c8f405ec722f9967eec5419200176ef7775e43d3c2ab5d3948fe7fd16b6de331680b40ff37040eaf06"
395                )),
396                c1: Bls12_381Fp(hex!(
397                    "09cce3edfb8410c8f405ec722f9967eec5419200176ef7775e43d3c2ab5d3948fe7fd16b6de331680b40ff37040eaf06"
398                ))
399            },
400            Fp2 {
401                c0: Bls12_381Fp(hex!(
402                    "fffffeffffff012e02000a6213d817de8896f8e63ba9b3ddea770f6a07c669ba51ce76df2f67195f0000000000000000"
403                )),
404                c1: Bls12_381Fp(hex!(
405                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
406                ))
407            },
408            Fp2 {
409                c0: Bls12_381Fp(hex!(
410                    "f34adc6d128af72cc27e6c4dc15a2d285f3cf671c98e0cec6fb3c7b68747a154b89f1f2302e9e98832e0c4362b3efc00"
411                )),
412                c1: Bls12_381Fp(hex!(
413                    "b85f2392ed75078d3d81e7633da57ef6c4b9ba84d743247b4f5fbd3cfd03d60f1f0d2c20b4be31c26706bb02bfd30419"
414                ))
415            },
416        ],
417        [
418            Fp2 {
419                c0: Bls12_381Fp(hex!(
420                    "aaaafffffffffeb9ffff53b1feffab1e24f6b0f6a0d23067bf1285f3844b7764d7ac4b43b6a71b4b9ae67f39ea11011a"
421                )),
422                c1: Bls12_381Fp(hex!(
423                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
424                ))
425            },
426            Fp2 {
427                c0: Bls12_381Fp(hex!(
428                    "010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
429                )),
430                c1: Bls12_381Fp(hex!(
431                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
432                ))
433            },
434            Fp2 {
435                c0: Bls12_381Fp(hex!(
436                    "aaaafffffffffeb9ffff53b1feffab1e24f6b0f6a0d23067bf1285f3844b7764d7ac4b43b6a71b4b9ae67f39ea11011a"
437                )),
438                c1: Bls12_381Fp(hex!(
439                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
440                ))
441            },
442            Fp2 {
443                c0: Bls12_381Fp(hex!(
444                    "010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
445                )),
446                c1: Bls12_381Fp(hex!(
447                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
448                ))
449            },
450            Fp2 {
451                c0: Bls12_381Fp(hex!(
452                    "aaaafffffffffeb9ffff53b1feffab1e24f6b0f6a0d23067bf1285f3844b7764d7ac4b43b6a71b4b9ae67f39ea11011a"
453                )),
454                c1: Bls12_381Fp(hex!(
455                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
456                ))
457            },
458        ],
459        [
460            Fp2 {
461                c0: Bls12_381Fp(hex!(
462                    "f34adc6d128af72cc27e6c4dc15a2d285f3cf671c98e0cec6fb3c7b68747a154b89f1f2302e9e98832e0c4362b3efc00"
463                )),
464                c1: Bls12_381Fp(hex!(
465                    "b85f2392ed75078d3d81e7633da57ef6c4b9ba84d743247b4f5fbd3cfd03d60f1f0d2c20b4be31c26706bb02bfd30419"
466                ))
467            },
468            Fp2 {
469                c0: Bls12_381Fp(hex!(
470                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
471                )),
472                c1: Bls12_381Fp(hex!(
473                    "acaa00000000fd8bfdff494feb2794409b5fb80f65297d89d49a75897d850daa85ded463864002ec99e67f39ea11011a"
474                ))
475            },
476            Fp2 {
477                c0: Bls12_381Fp(hex!(
478                    "a2de1b12047beef10afa673ecf6644305eb41ef6896439ef60cfb130d9ed3d1cd92c7ad748c4e9e28ea68001e6035213"
479                )),
480                c1: Bls12_381Fp(hex!(
481                    "a2de1b12047beef10afa673ecf6644305eb41ef6896439ef60cfb130d9ed3d1cd92c7ad748c4e9e28ea68001e6035213"
482                ))
483            },
484            Fp2 {
485                c0: Bls12_381Fp(hex!(
486                    "adaa00000000fd8bfdff494feb2794409b5fb80f65297d89d49a75897d850daa85ded463864002ec99e67f39ea11011a"
487                )),
488                c1: Bls12_381Fp(hex!(
489                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
490                ))
491            },
492            Fp2 {
493                c0: Bls12_381Fp(hex!(
494                    "9529f87f1605e61ecd78d48b90c17158bdf0146853f345dbd08279e76035df7091cc99fa4aadd36bc186453811424e14"
495                )),
496                c1: Bls12_381Fp(hex!(
497                    "16810780e9fa189b32877f256e3e3ac666059c8e4ddfea8bee8f0b0c241698f345e0b1486bfa47dfd85f3a01d9cfb205"
498                ))
499            },
500        ],
501        [
502            Fp2 {
503                c0: Bls12_381Fp(hex!(
504                    "acaa00000000fd8bfdff494feb2794409b5fb80f65297d89d49a75897d850daa85ded463864002ec99e67f39ea11011a"
505                )),
506                c1: Bls12_381Fp(hex!(
507                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
508                ))
509            },
510            Fp2 {
511                c0: Bls12_381Fp(hex!(
512                    "fefffeffffff012e02000a6213d817de8896f8e63ba9b3ddea770f6a07c669ba51ce76df2f67195f0000000000000000"
513                )),
514                c1: Bls12_381Fp(hex!(
515                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
516                ))
517            },
518            Fp2 {
519                c0: Bls12_381Fp(hex!(
520                    "010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
521                )),
522                c1: Bls12_381Fp(hex!(
523                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
524                ))
525            },
526            Fp2 {
527                c0: Bls12_381Fp(hex!(
528                    "acaa00000000fd8bfdff494feb2794409b5fb80f65297d89d49a75897d850daa85ded463864002ec99e67f39ea11011a"
529                )),
530                c1: Bls12_381Fp(hex!(
531                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
532                ))
533            },
534            Fp2 {
535                c0: Bls12_381Fp(hex!(
536                    "fefffeffffff012e02000a6213d817de8896f8e63ba9b3ddea770f6a07c669ba51ce76df2f67195f0000000000000000"
537                )),
538                c1: Bls12_381Fp(hex!(
539                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
540                ))
541            },
542        ],
543        [
544            Fp2 {
545                c0: Bls12_381Fp(hex!(
546                    "09cce3edfb8410c8f405ec722f9967eec5419200176ef7775e43d3c2ab5d3948fe7fd16b6de331680b40ff37040eaf06"
547                )),
548                c1: Bls12_381Fp(hex!(
549                    "a2de1b12047beef10afa673ecf6644305eb41ef6896439ef60cfb130d9ed3d1cd92c7ad748c4e9e28ea68001e6035213"
550                ))
551            },
552            Fp2 {
553                c0: Bls12_381Fp(hex!(
554                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
555                )),
556                c1: Bls12_381Fp(hex!(
557                    "010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
558                ))
559            },
560            Fp2 {
561                c0: Bls12_381Fp(hex!(
562                    "09cce3edfb8410c8f405ec722f9967eec5419200176ef7775e43d3c2ab5d3948fe7fd16b6de331680b40ff37040eaf06"
563                )),
564                c1: Bls12_381Fp(hex!(
565                    "09cce3edfb8410c8f405ec722f9967eec5419200176ef7775e43d3c2ab5d3948fe7fd16b6de331680b40ff37040eaf06"
566                ))
567            },
568            Fp2 {
569                c0: Bls12_381Fp(hex!(
570                    "aaaafffffffffeb9ffff53b1feffab1e24f6b0f6a0d23067bf1285f3844b7764d7ac4b43b6a71b4b9ae67f39ea11011a"
571                )),
572                c1: Bls12_381Fp(hex!(
573                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
574                ))
575            },
576            Fp2 {
577                c0: Bls12_381Fp(hex!(
578                    "a2de1b12047beef10afa673ecf6644305eb41ef6896439ef60cfb130d9ed3d1cd92c7ad748c4e9e28ea68001e6035213"
579                )),
580                c1: Bls12_381Fp(hex!(
581                    "09cce3edfb8410c8f405ec722f9967eec5419200176ef7775e43d3c2ab5d3948fe7fd16b6de331680b40ff37040eaf06"
582                ))
583            },
584        ],
585        [
586            Fp2 {
587                c0: Bls12_381Fp(hex!(
588                    "adaa00000000fd8bfdff494feb2794409b5fb80f65297d89d49a75897d850daa85ded463864002ec99e67f39ea11011a"
589                )),
590                c1: Bls12_381Fp(hex!(
591                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
592                ))
593            },
594            Fp2 {
595                c0: Bls12_381Fp(hex!(
596                    "acaa00000000fd8bfdff494feb2794409b5fb80f65297d89d49a75897d850daa85ded463864002ec99e67f39ea11011a"
597                )),
598                c1: Bls12_381Fp(hex!(
599                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
600                ))
601            },
602            Fp2 {
603                c0: Bls12_381Fp(hex!(
604                    "aaaafffffffffeb9ffff53b1feffab1e24f6b0f6a0d23067bf1285f3844b7764d7ac4b43b6a71b4b9ae67f39ea11011a"
605                )),
606                c1: Bls12_381Fp(hex!(
607                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
608                ))
609            },
610            Fp2 {
611                c0: Bls12_381Fp(hex!(
612                    "fefffeffffff012e02000a6213d817de8896f8e63ba9b3ddea770f6a07c669ba51ce76df2f67195f0000000000000000"
613                )),
614                c1: Bls12_381Fp(hex!(
615                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
616                ))
617            },
618            Fp2 {
619                c0: Bls12_381Fp(hex!(
620                    "fffffeffffff012e02000a6213d817de8896f8e63ba9b3ddea770f6a07c669ba51ce76df2f67195f0000000000000000"
621                )),
622                c1: Bls12_381Fp(hex!(
623                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
624                ))
625            },
626        ],
627        [
628            Fp2 {
629                c0: Bls12_381Fp(hex!(
630                    "16810780e9fa189b32877f256e3e3ac666059c8e4ddfea8bee8f0b0c241698f345e0b1486bfa47dfd85f3a01d9cfb205"
631                )),
632                c1: Bls12_381Fp(hex!(
633                    "9529f87f1605e61ecd78d48b90c17158bdf0146853f345dbd08279e76035df7091cc99fa4aadd36bc186453811424e14"
634                ))
635            },
636            Fp2 {
637                c0: Bls12_381Fp(hex!(
638                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
639                )),
640                c1: Bls12_381Fp(hex!(
641                    "fefffeffffff012e02000a6213d817de8896f8e63ba9b3ddea770f6a07c669ba51ce76df2f67195f0000000000000000"
642                ))
643            },
644            Fp2 {
645                c0: Bls12_381Fp(hex!(
646                    "a2de1b12047beef10afa673ecf6644305eb41ef6896439ef60cfb130d9ed3d1cd92c7ad748c4e9e28ea68001e6035213"
647                )),
648                c1: Bls12_381Fp(hex!(
649                    "a2de1b12047beef10afa673ecf6644305eb41ef6896439ef60cfb130d9ed3d1cd92c7ad748c4e9e28ea68001e6035213"
650                ))
651            },
652            Fp2 {
653                c0: Bls12_381Fp(hex!(
654                    "fffffeffffff012e02000a6213d817de8896f8e63ba9b3ddea770f6a07c669ba51ce76df2f67195f0000000000000000"
655                )),
656                c1: Bls12_381Fp(hex!(
657                    "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
658                ))
659            },
660            Fp2 {
661                c0: Bls12_381Fp(hex!(
662                    "b85f2392ed75078d3d81e7633da57ef6c4b9ba84d743247b4f5fbd3cfd03d60f1f0d2c20b4be31c26706bb02bfd30419"
663                )),
664                c1: Bls12_381Fp(hex!(
665                    "f34adc6d128af72cc27e6c4dc15a2d285f3cf671c98e0cec6fb3c7b68747a154b89f1f2302e9e98832e0c4362b3efc00"
666                ))
667            },
668        ],
669    ];
670}
671
672impl Bls12_381 {
673    // FINAL_EXPONENT = (p^12 - 1) / r in big-endian
674    // Validated by a test in test.rs
675    pub const FINAL_EXPONENT: [u8; 540] = hex!(
676        "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"
677    );
678}
openvm_pairing_guest/bls12_381/mod.rs

openvm_pairing_guest/bls12_381/
mod.rs
