snarkvm_fields/
fp6_3over2.rs

1// Copyright (c) 2019-2025 Provable Inc.
2// This file is part of the snarkVM library.
3
4// Licensed under the Apache License, Version 2.0 (the "License");
5// you may not use this file except in compliance with the License.
6// You may obtain a copy of the License at:
7
8// http://www.apache.org/licenses/LICENSE-2.0
9
10// Unless required by applicable law or agreed to in writing, software
11// distributed under the License is distributed on an "AS IS" BASIS,
12// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
13// See the License for the specific language governing permissions and
14// limitations under the License.
15
16use crate::{Field, Fp2, Fp2Parameters, One, Zero};
17use snarkvm_utilities::{
18    FromBytes,
19    ToBits,
20    ToBytes,
21    rand::Uniform,
22    serialize::{SerializationError, *},
23};
24
25use rand::{
26    Rng,
27    distributions::{Distribution, Standard},
28};
29use serde::{Deserialize, Serialize};
30use std::{
31    cmp::Ordering,
32    fmt::Debug,
33    hash::Hash,
34    io::{Read, Result as IoResult, Write},
35    ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign},
36};
37
38pub trait Fp6Parameters: 'static + Copy + Clone + Default + Debug + PartialEq + Eq + Hash + Send + Sync {
39    type Fp2Params: Fp2Parameters;
40
41    /// Coefficients for the Frobenius automorphism.
42    const FROBENIUS_COEFF_FP6_C1: [Fp2<Self::Fp2Params>; 6];
43    const FROBENIUS_COEFF_FP6_C2: [Fp2<Self::Fp2Params>; 6];
44
45    const NONRESIDUE: Fp2<Self::Fp2Params>;
46
47    #[inline(always)]
48    fn mul_fp2_by_nonresidue(fe: &Fp2<Self::Fp2Params>) -> Fp2<Self::Fp2Params> {
49        Self::NONRESIDUE * fe
50    }
51}
52
53/// An element of Fp6, represented by c0 + c1 * v + c2 * v^(2).
54#[derive(Copy, Clone, Debug, Default, PartialEq, Eq, Hash, Serialize, Deserialize)]
55pub struct Fp6<P: Fp6Parameters> {
56    pub c0: Fp2<P::Fp2Params>,
57    pub c1: Fp2<P::Fp2Params>,
58    pub c2: Fp2<P::Fp2Params>,
59}
60
61impl<P: Fp6Parameters> Fp6<P> {
62    /// Initializes an element of `Fp6` from 3 `Fp2` elements.
63    pub const fn new(c0: Fp2<P::Fp2Params>, c1: Fp2<P::Fp2Params>, c2: Fp2<P::Fp2Params>) -> Self {
64        Self { c0, c1, c2 }
65    }
66
67    pub fn mul_by_fp(&mut self, element: &<P::Fp2Params as Fp2Parameters>::Fp) {
68        self.c0.mul_by_fp(element);
69        self.c1.mul_by_fp(element);
70        self.c2.mul_by_fp(element);
71    }
72
73    pub fn mul_by_fp2(&mut self, element: &Fp2<P::Fp2Params>) {
74        self.c0.mul_assign(element);
75        self.c1.mul_assign(element);
76        self.c2.mul_assign(element);
77    }
78
79    pub fn mul_by_1(&mut self, c1: &Fp2<P::Fp2Params>) {
80        let mut b_b = self.c1;
81        b_b.mul_assign(c1);
82
83        let mut t1 = *c1;
84        {
85            let mut tmp = self.c1;
86            tmp.add_assign(self.c2);
87
88            t1.mul_assign(&tmp);
89            t1.sub_assign(&b_b);
90            t1 = P::mul_fp2_by_nonresidue(&t1);
91        }
92
93        let mut t2 = *c1;
94        {
95            let mut tmp = self.c0;
96            tmp.add_assign(self.c1);
97
98            t2.mul_assign(&tmp);
99            t2.sub_assign(&b_b);
100        }
101
102        self.c0 = t1;
103        self.c1 = t2;
104        self.c2 = b_b;
105    }
106
107    pub fn mul_by_01(&mut self, c0: &Fp2<P::Fp2Params>, c1: &Fp2<P::Fp2Params>) {
108        let mut a_a = self.c0;
109        let mut b_b = self.c1;
110        a_a.mul_assign(c0);
111        b_b.mul_assign(c1);
112
113        let mut t1 = *c1;
114        {
115            let mut tmp = self.c1;
116            tmp.add_assign(self.c2);
117
118            t1.mul_assign(&tmp);
119            t1.sub_assign(&b_b);
120            t1 = P::mul_fp2_by_nonresidue(&t1);
121            t1.add_assign(a_a);
122        }
123
124        let mut t3 = *c0;
125        {
126            let mut tmp = self.c0;
127            tmp.add_assign(self.c2);
128
129            t3.mul_assign(&tmp);
130            t3.sub_assign(&a_a);
131            t3.add_assign(b_b);
132        }
133
134        let mut t2 = *c0;
135        t2.add_assign(c1);
136        {
137            let mut tmp = self.c0;
138            tmp.add_assign(self.c1);
139
140            t2.mul_assign(&tmp);
141            t2.sub_assign(&a_a);
142            t2.sub_assign(&b_b);
143        }
144
145        self.c0 = t1;
146        self.c1 = t2;
147        self.c2 = t3;
148    }
149}
150
151impl<P: Fp6Parameters> Zero for Fp6<P> {
152    fn zero() -> Self {
153        Self::new(Fp2::zero(), Fp2::zero(), Fp2::zero())
154    }
155
156    fn is_zero(&self) -> bool {
157        self.c0.is_zero() && self.c1.is_zero() && self.c2.is_zero()
158    }
159}
160
161impl<P: Fp6Parameters> One for Fp6<P> {
162    fn one() -> Self {
163        Self::new(Fp2::one(), Fp2::zero(), Fp2::zero())
164    }
165
166    fn is_one(&self) -> bool {
167        self.c0.is_one() && self.c1.is_zero() && self.c2.is_zero()
168    }
169}
170
171impl<P: Fp6Parameters> Field for Fp6<P> {
172    type BasePrimeField = <Fp2<P::Fp2Params> as Field>::BasePrimeField;
173
174    fn from_base_prime_field(other: Self::BasePrimeField) -> Self {
175        Self::new(Fp2::from_base_prime_field(other), Fp2::zero(), Fp2::zero())
176    }
177
178    #[inline]
179    fn characteristic<'a>() -> &'a [u64] {
180        Fp2::<P::Fp2Params>::characteristic()
181    }
182
183    fn double(&self) -> Self {
184        let mut result = *self;
185        result.double_in_place();
186        result
187    }
188
189    fn double_in_place(&mut self) {
190        self.c0.double_in_place();
191        self.c1.double_in_place();
192        self.c2.double_in_place();
193    }
194
195    #[inline]
196    fn from_random_bytes_with_flags<F: Flags>(bytes: &[u8]) -> Option<(Self, F)> {
197        let split_at = bytes.len() / 3;
198        if let Some(c0) = Fp2::<P::Fp2Params>::from_random_bytes(&bytes[..split_at]) {
199            if let Some(c1) = Fp2::<P::Fp2Params>::from_random_bytes(&bytes[split_at..2 * split_at]) {
200                if let Some((c2, flags)) =
201                    Fp2::<P::Fp2Params>::from_random_bytes_with_flags::<F>(&bytes[2 * split_at..])
202                {
203                    return Some((Fp6::new(c0, c1, c2), flags));
204                }
205            }
206        }
207        None
208    }
209
210    #[inline]
211    fn from_random_bytes(bytes: &[u8]) -> Option<Self> {
212        Self::from_random_bytes_with_flags::<EmptyFlags>(bytes).map(|f| f.0)
213    }
214
215    fn square(&self) -> Self {
216        let mut result = *self;
217        result.square_in_place();
218        result
219    }
220
221    fn square_in_place(&mut self) -> &mut Self {
222        let s0 = self.c0.square();
223        let s1 = (self.c0 * self.c1).double();
224        let s2 = (self.c0 - self.c1 + self.c2).square();
225        let s3 = (self.c1 * self.c2).double();
226        let s4 = self.c2.square();
227
228        self.c0 = s0 + P::mul_fp2_by_nonresidue(&s3);
229        self.c1 = s1 + P::mul_fp2_by_nonresidue(&s4);
230        self.c2 = s1 + s2 + s3 - s0 - s4;
231
232        self
233    }
234
235    fn inverse(&self) -> Option<Self> {
236        if self.is_zero() {
237            None
238        } else {
239            let mut c0 = self.c2;
240            c0 = P::mul_fp2_by_nonresidue(&c0);
241            c0.mul_assign(&self.c1);
242            c0 = c0.neg();
243            {
244                let mut c0s = self.c0;
245                c0s.square_in_place();
246                c0.add_assign(c0s);
247            }
248            let mut c1 = self.c2;
249            c1.square_in_place();
250            c1 = P::mul_fp2_by_nonresidue(&c1);
251            {
252                let mut c01 = self.c0;
253                c01.mul_assign(&self.c1);
254                c1.sub_assign(&c01);
255            }
256            let mut c2 = self.c1;
257            c2.square_in_place();
258            {
259                let mut c02 = self.c0;
260                c02.mul_assign(&self.c2);
261                c2.sub_assign(&c02);
262            }
263
264            let mut tmp1 = self.c2;
265            tmp1.mul_assign(&c1);
266            let mut tmp2 = self.c1;
267            tmp2.mul_assign(&c2);
268            tmp1.add_assign(tmp2);
269            tmp1 = P::mul_fp2_by_nonresidue(&tmp1);
270            tmp2 = self.c0;
271            tmp2.mul_assign(&c0);
272            tmp1.add_assign(tmp2);
273
274            tmp1.inverse().map(|t| Self::new(t * c0, t * c1, t * c2))
275        }
276    }
277
278    fn inverse_in_place(&mut self) -> Option<&mut Self> {
279        if let Some(inverse) = self.inverse() {
280            *self = inverse;
281            Some(self)
282        } else {
283            None
284        }
285    }
286
287    fn frobenius_map(&mut self, power: usize) {
288        self.c0.frobenius_map(power);
289        self.c1.frobenius_map(power);
290        self.c2.frobenius_map(power);
291
292        self.c1.mul_assign(&P::FROBENIUS_COEFF_FP6_C1[power % 6]);
293        self.c2.mul_assign(&P::FROBENIUS_COEFF_FP6_C2[power % 6]);
294    }
295}
296
297impl<P: Fp6Parameters> std::fmt::Display for Fp6<P> {
298    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
299        write!(f, "Fq6_3over2({} + {} * v, {} * v^2)", self.c0, self.c1, self.c2)
300    }
301}
302
303impl<P: Fp6Parameters> Distribution<Fp6<P>> for Standard {
304    #[inline]
305    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Fp6<P> {
306        Fp6::new(Uniform::rand(rng), Uniform::rand(rng), Uniform::rand(rng))
307    }
308}
309
310impl<P: Fp6Parameters> Neg for Fp6<P> {
311    type Output = Self;
312
313    #[inline]
314    fn neg(self) -> Self {
315        let mut copy = Self::zero();
316        copy.c0 = self.c0.neg();
317        copy.c1 = self.c1.neg();
318        copy.c2 = self.c2.neg();
319        copy
320    }
321}
322
323impl_add_sub_from_field_ref!(Fp6, Fp6Parameters);
324impl_mul_div_from_field_ref!(Fp6, Fp6Parameters);
325
326impl<P: Fp6Parameters> Add<&'_ Self> for Fp6<P> {
327    type Output = Self;
328
329    #[inline]
330    fn add(self, other: &Self) -> Self {
331        let mut result = self;
332        result.add_assign(other);
333        result
334    }
335}
336
337impl<P: Fp6Parameters> Sub<&'_ Self> for Fp6<P> {
338    type Output = Self;
339
340    #[inline]
341    fn sub(self, other: &Self) -> Self {
342        let mut result = self;
343        result.sub_assign(&other);
344        result
345    }
346}
347
348impl<P: Fp6Parameters> Mul<&'_ Self> for Fp6<P> {
349    type Output = Self;
350
351    #[inline]
352    fn mul(self, other: &Self) -> Self {
353        let mut result = self;
354        result.mul_assign(&other);
355        result
356    }
357}
358
359impl<P: Fp6Parameters> Div<&'_ Self> for Fp6<P> {
360    type Output = Self;
361
362    #[inline]
363    fn div(self, other: &Self) -> Self {
364        let mut result = self;
365        result.mul_assign(&other.inverse().unwrap());
366        result
367    }
368}
369
370impl<P: Fp6Parameters> AddAssign<&'_ Self> for Fp6<P> {
371    #[inline]
372    fn add_assign(&mut self, other: &Self) {
373        self.c0 += &other.c0;
374        self.c1 += &other.c1;
375        self.c2 += &other.c2;
376    }
377}
378
379impl<P: Fp6Parameters> SubAssign<&'_ Self> for Fp6<P> {
380    #[inline]
381    fn sub_assign(&mut self, other: &Self) {
382        self.c0 -= &other.c0;
383        self.c1 -= &other.c1;
384        self.c2 -= &other.c2;
385    }
386}
387
388impl<P: Fp6Parameters> MulAssign<&'_ Self> for Fp6<P> {
389    #[inline]
390    fn mul_assign(&mut self, other: &Self) {
391        let v0 = self.c0 * other.c0;
392        let v1 = self.c1 * other.c1;
393        let v2 = self.c2 * other.c2;
394
395        let c0 = P::mul_fp2_by_nonresidue(&((self.c1 + self.c2) * (other.c1 + other.c2) - v1 - v2)) + v0;
396        let c1 = (self.c0 + self.c1) * (other.c0 + other.c1) - v0 - v1 + P::mul_fp2_by_nonresidue(&v2);
397        let c2 = (self.c0 + self.c2) * (other.c0 + other.c2) - v0 - v2 + v1;
398
399        self.c0 = c0;
400        self.c1 = c1;
401        self.c2 = c2;
402    }
403}
404
405impl<P: Fp6Parameters> DivAssign<&'_ Self> for Fp6<P> {
406    #[inline]
407    fn div_assign(&mut self, other: &Self) {
408        self.mul_assign(&other.inverse().unwrap());
409    }
410}
411
412impl<P: Fp6Parameters> From<&'_ [bool]> for Fp6<P> {
413    fn from(_bits: &[bool]) -> Self {
414        unimplemented!()
415    }
416}
417
418/// `Fp3` elements are ordered lexicographically.
419impl<P: Fp6Parameters> Ord for Fp6<P> {
420    #[inline(always)]
421    fn cmp(&self, other: &Self) -> Ordering {
422        let c2_cmp = self.c2.cmp(&other.c2);
423        let c1_cmp = self.c1.cmp(&other.c1);
424        let c0_cmp = self.c0.cmp(&other.c0);
425        match c2_cmp {
426            Ordering::Equal => match c1_cmp {
427                Ordering::Equal => c0_cmp,
428                _ => c1_cmp,
429            },
430            _ => c2_cmp,
431        }
432    }
433}
434
435impl<P: Fp6Parameters> PartialOrd for Fp6<P> {
436    #[inline(always)]
437    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
438        Some(self.cmp(other))
439    }
440}
441
442impl<P: Fp6Parameters> From<u128> for Fp6<P> {
443    fn from(other: u128) -> Self {
444        Self::new(other.into(), Fp2::zero(), Fp2::zero())
445    }
446}
447
448impl<P: Fp6Parameters> From<u64> for Fp6<P> {
449    fn from(other: u64) -> Self {
450        Self::new(other.into(), Fp2::zero(), Fp2::zero())
451    }
452}
453
454impl<P: Fp6Parameters> From<u32> for Fp6<P> {
455    fn from(other: u32) -> Self {
456        Self::new(other.into(), Fp2::zero(), Fp2::zero())
457    }
458}
459
460impl<P: Fp6Parameters> From<u16> for Fp6<P> {
461    fn from(other: u16) -> Self {
462        Self::new(other.into(), Fp2::zero(), Fp2::zero())
463    }
464}
465
466impl<P: Fp6Parameters> From<u8> for Fp6<P> {
467    fn from(other: u8) -> Self {
468        Self::new(other.into(), Fp2::zero(), Fp2::zero())
469    }
470}
471
472impl<P: Fp6Parameters> ToBits for Fp6<P> {
473    fn write_bits_le(&self, vec: &mut Vec<bool>) {
474        self.c0.write_bits_le(vec);
475        self.c1.write_bits_le(vec);
476        self.c2.write_bits_le(vec);
477    }
478
479    fn write_bits_be(&self, vec: &mut Vec<bool>) {
480        self.c0.write_bits_be(vec);
481        self.c1.write_bits_be(vec);
482        self.c2.write_bits_be(vec);
483    }
484}
485
486impl<P: Fp6Parameters> ToBytes for Fp6<P> {
487    #[inline]
488    fn write_le<W: Write>(&self, mut writer: W) -> IoResult<()> {
489        self.c0.write_le(&mut writer)?;
490        self.c1.write_le(&mut writer)?;
491        self.c2.write_le(&mut writer)
492    }
493}
494
495impl<P: Fp6Parameters> FromBytes for Fp6<P> {
496    #[inline]
497    fn read_le<R: Read>(mut reader: R) -> IoResult<Self> {
498        let c0 = Fp2::read_le(&mut reader)?;
499        let c1 = Fp2::read_le(&mut reader)?;
500        let c2 = Fp2::read_le(&mut reader)?;
501        Ok(Fp6::new(c0, c1, c2))
502    }
503}
504
505impl<P: Fp6Parameters> CanonicalSerializeWithFlags for Fp6<P> {
506    #[inline]
507    fn serialize_with_flags<W: Write, F: Flags>(&self, mut writer: W, flags: F) -> Result<(), SerializationError> {
508        CanonicalSerialize::serialize_uncompressed(&self.c0, &mut writer)?;
509        CanonicalSerialize::serialize_uncompressed(&self.c1, &mut writer)?;
510        self.c2.serialize_with_flags(writer, flags)?;
511        Ok(())
512    }
513
514    fn serialized_size_with_flags<F: Flags>(&self) -> usize {
515        self.c0.uncompressed_size() + self.c1.uncompressed_size() + self.c2.serialized_size_with_flags::<F>()
516    }
517}
518
519impl<P: Fp6Parameters> CanonicalSerialize for Fp6<P> {
520    #[inline]
521    fn serialize_with_mode<W: Write>(&self, writer: W, _compress: Compress) -> Result<(), SerializationError> {
522        self.serialize_with_flags(writer, EmptyFlags)
523    }
524
525    #[inline]
526    fn serialized_size(&self, compress: Compress) -> usize {
527        self.c0.serialized_size(compress) + self.c1.serialized_size(compress) + self.c2.serialized_size(compress)
528    }
529}
530
531impl<P: Fp6Parameters> Valid for Fp6<P> {
532    fn check(&self) -> Result<(), snarkvm_utilities::SerializationError> {
533        Ok(())
534    }
535
536    fn batch_check<'a>(_batch: impl Iterator<Item = &'a Self>) -> Result<(), snarkvm_utilities::SerializationError>
537    where
538        Self: 'a,
539    {
540        Ok(())
541    }
542}
543
544impl<P: Fp6Parameters> CanonicalDeserializeWithFlags for Fp6<P> {
545    #[inline]
546    fn deserialize_with_flags<R: Read, F: Flags>(mut reader: R) -> Result<(Self, F), SerializationError> {
547        let c0 = CanonicalDeserialize::deserialize_uncompressed(&mut reader)?;
548        let c1 = CanonicalDeserialize::deserialize_uncompressed(&mut reader)?;
549        let (c2, flags): (_, _) = CanonicalDeserializeWithFlags::deserialize_with_flags(&mut reader)?;
550        Ok((Fp6::new(c0, c1, c2), flags))
551    }
552}
553
554impl<P: Fp6Parameters> CanonicalDeserialize for Fp6<P> {
555    #[inline]
556    fn deserialize_with_mode<R: Read>(
557        mut reader: R,
558        compress: Compress,
559        validate: Validate,
560    ) -> Result<Self, SerializationError> {
561        let c0 = CanonicalDeserialize::deserialize_with_mode(&mut reader, compress, validate)?;
562        let c1 = CanonicalDeserialize::deserialize_with_mode(&mut reader, compress, validate)?;
563        let c2 = CanonicalDeserialize::deserialize_with_mode(&mut reader, compress, validate)?;
564        Ok(Fp6::new(c0, c1, c2))
565    }
566}
snarkvm_fields/fp6_3over2.rs

snarkvm_fields/
fp6_3over2.rs
