ark-r1cs-std/r1cs-std/src/groups/curves/twisted_edwards/mod.rs
r1cs-std/src/groups/curves/twisted_edwards/mod.rsRaw
1use algebra::{
2 curves::{
3 twisted_edwards_extended::{GroupAffine as TEAffine, GroupProjective as TEProjective},
4 AffineCurve, MontgomeryModelParameters, ProjectiveCurve, TEModelParameters,
5 },
6 BigInteger, BitIteratorBE, Field, One, PrimeField, Zero,
7};
8
9use r1cs_core::{ConstraintSystemRef, Namespace, SynthesisError};
10
11use crate::{prelude::*, Vec};
12
13use core::{borrow::Borrow, marker::PhantomData};
14
15#[derive(Derivative)]
16#[derivative(Debug, Clone)]
17#[must_use]
18pub struct MontgomeryAffineVar<
19 P: TEModelParameters,
20 F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>,
21> where
22 for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>,
23{
24 pub x: F,
25 pub y: F,
26 #[derivative(Debug = "ignore")]
27 _params: PhantomData<P>,
28}
29
30mod montgomery_affine_impl {
31 use super::*;
32 use algebra::{twisted_edwards_extended::GroupAffine, Field};
33 use core::ops::Add;
34
35 impl<P, F> R1CSVar<<P::BaseField as Field>::BasePrimeField> for MontgomeryAffineVar<P, F>
36 where
37 P: TEModelParameters,
38 F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>,
39 for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>,
40 {
41 type Value = (P::BaseField, P::BaseField);
42
43 fn cs(&self) -> Option<ConstraintSystemRef<<P::BaseField as Field>::BasePrimeField>> {
44 self.x.cs().or(self.y.cs())
45 }
46
47 fn value(&self) -> Result<Self::Value, SynthesisError> {
48 let x = self.x.value()?;
49 let y = self.y.value()?;
50 Ok((x, y))
51 }
52 }
53
54 impl<
55 P: TEModelParameters,
56 F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>,
57 > MontgomeryAffineVar<P, F>
58 where
59 for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>,
60 {
61 pub fn new(x: F, y: F) -> Self {
62 Self {
63 x,
64 y,
65 _params: PhantomData,
66 }
67 }
68
69 pub fn from_edwards_to_coords(
70 p: &TEAffine<P>,
71 ) -> Result<(P::BaseField, P::BaseField), SynthesisError> {
72 let montgomery_point: GroupAffine<P> = if p.y == P::BaseField::one() {
73 GroupAffine::zero()
74 } else if p.x == P::BaseField::zero() {
75 GroupAffine::new(P::BaseField::zero(), P::BaseField::zero())
76 } else {
77 let u =
78 (P::BaseField::one() + &p.y) * &(P::BaseField::one() - &p.y).inverse().unwrap();
79 let v = u * &p.x.inverse().unwrap();
80 GroupAffine::new(u, v)
81 };
82
83 Ok((montgomery_point.x, montgomery_point.y))
84 }
85
86 pub fn new_witness_from_edwards(
87 cs: ConstraintSystemRef<<P::BaseField as Field>::BasePrimeField>,
88 p: &TEAffine<P>,
89 ) -> Result<Self, SynthesisError> {
90 let montgomery_coords = Self::from_edwards_to_coords(p)?;
91 let u = F::new_witness(cs.ns("u"), || Ok(montgomery_coords.0))?;
92 let v = F::new_witness(cs.ns("v"), || Ok(montgomery_coords.1))?;
93 Ok(Self::new(u, v))
94 }
95
96 pub fn into_edwards(&self) -> Result<AffineVar<P, F>, SynthesisError> {
97 let cs = self.cs().unwrap_or(ConstraintSystemRef::None);
98 // Compute u = x / y
99 let u = F::new_witness(cs.ns("u"), || {
100 let y_inv = self
101 .y
102 .value()?
103 .inverse()
104 .ok_or(SynthesisError::DivisionByZero)?;
105 Ok(self.x.value()? * &y_inv)
106 })?;
107
108 u.mul_equals(&self.y, &self.x)?;
109
110 let v = F::new_witness(cs.ns("v"), || {
111 let mut t0 = self.x.value()?;
112 let mut t1 = t0;
113 t0 -= &P::BaseField::one();
114 t1 += &P::BaseField::one();
115
116 Ok(t0 * &t1.inverse().ok_or(SynthesisError::DivisionByZero)?)
117 })?;
118
119 let xplusone = &self.x + P::BaseField::one();
120 let xminusone = &self.x - P::BaseField::one();
121 v.mul_equals(&xplusone, &xminusone)?;
122
123 Ok(AffineVar::new(u, v))
124 }
125 }
126
127 impl<'a, P, F> Add<&'a MontgomeryAffineVar<P, F>> for MontgomeryAffineVar<P, F>
128 where
129 P: TEModelParameters,
130 F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>,
131 for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,
132 {
133 type Output = MontgomeryAffineVar<P, F>;
134 fn add(self, other: &'a Self) -> Self::Output {
135 let cs = [&self, other].cs();
136 let mode = if cs.is_none() || matches!(cs, Some(ConstraintSystemRef::None)) {
137 AllocationMode::Constant
138 } else {
139 AllocationMode::Witness
140 };
141 let cs = cs.unwrap_or(ConstraintSystemRef::None);
142
143 let coeff_b = P::MontgomeryModelParameters::COEFF_B;
144 let coeff_a = P::MontgomeryModelParameters::COEFF_A;
145
146 let lambda = F::new_variable(
147 cs.ns("lambda"),
148 || {
149 let n = other.y.value()? - &self.y.value()?;
150 let d = other.x.value()? - &self.x.value()?;
151 Ok(n * &d.inverse().ok_or(SynthesisError::DivisionByZero)?)
152 },
153 mode,
154 )
155 .unwrap();
156 let lambda_n = &other.y - &self.y;
157 let lambda_d = &other.x - &self.x;
158 lambda_d.mul_equals(&lambda, &lambda_n).unwrap();
159
160 // Compute x'' = B*lambda^2 - A - x - x'
161 let xprime = F::new_variable(
162 cs.ns("xprime"),
163 || {
164 Ok(lambda.value()?.square() * &coeff_b
165 - &coeff_a
166 - &self.x.value()?
167 - &other.x.value()?)
168 },
169 mode,
170 )
171 .unwrap();
172
173 let xprime_lc = &self.x + &other.x + &xprime + coeff_a;
174 // (lambda) * (lambda) = (A + x + x' + x'')
175 let lambda_b = &lambda * coeff_b;
176 lambda_b.mul_equals(&lambda, &xprime_lc).unwrap();
177
178 let yprime = F::new_variable(
179 cs.ns("yprime"),
180 || {
181 Ok(-(self.y.value()?
182 + &(lambda.value()? * &(xprime.value()? - &self.x.value()?))))
183 },
184 mode,
185 )
186 .unwrap();
187
188 let xres = &self.x - &xprime;
189 let yres = &self.y + &yprime;
190 lambda.mul_equals(&xres, &yres).unwrap();
191 MontgomeryAffineVar::new(xprime, yprime)
192 }
193 }
194}
195
196#[derive(Derivative)]
197#[derivative(Debug, Clone)]
198#[must_use]
199pub struct AffineVar<
200 P: TEModelParameters,
201 F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>,
202> where
203 for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>,
204{
205 pub x: F,
206 pub y: F,
207 #[derivative(Debug = "ignore")]
208 _params: PhantomData<P>,
209}
210
211impl<P: TEModelParameters, F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>>
212 AffineVar<P, F>
213where
214 for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>,
215{
216 pub fn new(x: F, y: F) -> Self {
217 Self {
218 x,
219 y,
220 _params: PhantomData,
221 }
222 }
223
224 /// Allocates a new variable without performing an on-curve check, which is
225 /// useful if the variable is known to be on the curve (eg., if the point
226 /// is a constant or is a public input).
227 pub fn new_variable_omit_on_curve_check<T: Into<TEAffine<P>>>(
228 cs: impl Into<Namespace<<P::BaseField as Field>::BasePrimeField>>,
229 f: impl FnOnce() -> Result<T, SynthesisError>,
230 mode: AllocationMode,
231 ) -> Result<Self, SynthesisError> {
232 let ns = cs.into();
233 let cs = ns.cs();
234
235 let (x, y) = match f() {
236 Ok(ge) => {
237 let ge: TEAffine<P> = ge.into();
238 (Ok(ge.x), Ok(ge.y))
239 }
240 _ => (
241 Err(SynthesisError::AssignmentMissing),
242 Err(SynthesisError::AssignmentMissing),
243 ),
244 };
245
246 let x = F::new_variable(cs.ns("x"), || x, mode)?;
247 let y = F::new_variable(cs.ns("y"), || y, mode)?;
248
249 Ok(Self::new(x, y))
250 }
251}
252
253impl<P, F> R1CSVar<<P::BaseField as Field>::BasePrimeField> for AffineVar<P, F>
254where
255 P: TEModelParameters,
256 F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>,
257 for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>,
258{
259 type Value = TEProjective<P>;
260
261 fn cs(&self) -> Option<ConstraintSystemRef<<P::BaseField as Field>::BasePrimeField>> {
262 self.x.cs().or(self.y.cs())
263 }
264
265 #[inline]
266 fn value(&self) -> Result<TEProjective<P>, SynthesisError> {
267 let (x, y) = (self.x.value()?, self.y.value()?);
268 let result = TEAffine::new(x, y);
269 Ok(result.into())
270 }
271}
272
273impl<P, F> CurveVar<TEProjective<P>, <P::BaseField as Field>::BasePrimeField> for AffineVar<P, F>
274where
275 P: TEModelParameters,
276 F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>
277 + TwoBitLookupGadget<<P::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>
278 + ThreeBitCondNegLookupGadget<
279 <P::BaseField as Field>::BasePrimeField,
280 TableConstant = P::BaseField,
281 >,
282 for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>,
283{
284 fn constant(g: TEProjective<P>) -> Self {
285 let cs = ConstraintSystemRef::None;
286 Self::new_variable_omit_on_curve_check(cs, || Ok(g), AllocationMode::Constant).unwrap()
287 }
288
289 fn zero() -> Self {
290 Self::new(F::zero(), F::one())
291 }
292
293 fn is_zero(&self) -> Result<Boolean<<P::BaseField as Field>::BasePrimeField>, SynthesisError> {
294 self.x.is_zero()?.and(&self.x.is_one()?)
295 }
296
297 fn new_variable_omit_prime_order_check(
298 cs: impl Into<Namespace<<P::BaseField as Field>::BasePrimeField>>,
299 f: impl FnOnce() -> Result<TEProjective<P>, SynthesisError>,
300 mode: AllocationMode,
301 ) -> Result<Self, SynthesisError> {
302 let ns = cs.into();
303 let cs = ns.cs();
304
305 let g = Self::new_variable_omit_on_curve_check(cs, f, mode)?;
306
307 if mode != AllocationMode::Constant {
308 let d = P::COEFF_D;
309 let a = P::COEFF_A;
310 // Check that ax^2 + y^2 = 1 + dx^2y^2
311 // We do this by checking that ax^2 - 1 = y^2 * (dx^2 - 1)
312 let x2 = g.x.square()?;
313 let y2 = g.y.square()?;
314
315 let one = P::BaseField::one();
316 let d_x2_minus_one = &x2 * d - one;
317 let a_x2_minus_one = &x2 * a - one;
318
319 d_x2_minus_one.mul_equals(&y2, &a_x2_minus_one)?;
320 }
321 Ok(g)
322 }
323
324 /// Enforce that `self` is in the prime-order subgroup.
325 ///
326 /// Does so by multiplying by the prime order, and checking that the result
327 /// is unchanged.
328 fn enforce_prime_order(&self) -> Result<(), SynthesisError> {
329 let r_minus_1 = (-P::ScalarField::one()).into_repr();
330
331 let mut result = Self::zero();
332 for b in BitIteratorBE::without_leading_zeros(r_minus_1) {
333 result.double_in_place()?;
334
335 if b {
336 result += self;
337 }
338 }
339 self.negate()?.enforce_equal(&result)?;
340 Ok(())
341 }
342
343 #[inline]
344 fn double_in_place(&mut self) -> Result<(), SynthesisError> {
345 if let Some(cs) = self.cs() {
346 let a = P::COEFF_A;
347
348 // xy
349 let xy = &self.x * &self.y;
350 let x2 = self.x.square()?;
351 let y2 = self.y.square()?;
352
353 let a_x2 = &x2 * a;
354
355 // Compute x3 = (2xy) / (ax^2 + y^2)
356 let x3 = F::new_witness(cs.ns("x3"), || {
357 let t0 = xy.value()?.double();
358 let t1 = a * &x2.value()? + &y2.value()?;
359 Ok(t0 * &t1.inverse().ok_or(SynthesisError::DivisionByZero)?)
360 })?;
361
362 let a_x2_plus_y2 = &a_x2 + &y2;
363 let two_xy = xy.double()?;
364 x3.mul_equals(&a_x2_plus_y2, &two_xy)?;
365
366 // Compute y3 = (y^2 - ax^2) / (2 - ax^2 - y^2)
367 let two = P::BaseField::one().double();
368 let y3 = F::new_witness(cs.ns("y3"), || {
369 let a_x2 = a * &x2.value()?;
370 let t0 = y2.value()? - &a_x2;
371 let t1 = two - &a_x2 - &y2.value()?;
372 Ok(t0 * &t1.inverse().ok_or(SynthesisError::DivisionByZero)?)
373 })?;
374 let y2_minus_a_x2 = &y2 - &a_x2;
375 let two_minus_ax2_minus_y2 = (&a_x2 + &y2).negate()? + two;
376
377 y3.mul_equals(&two_minus_ax2_minus_y2, &y2_minus_a_x2)?;
378 self.x = x3;
379 self.y = y3;
380 } else {
381 let value = self.value()?;
382 *self = Self::constant(value.double());
383 }
384 Ok(())
385 }
386
387 fn negate(&self) -> Result<Self, SynthesisError> {
388 Ok(Self::new(self.x.negate()?, self.y.clone()))
389 }
390
391 fn precomputed_base_scalar_mul_le<'a, I, B>(
392 &mut self,
393 scalar_bits_with_base_powers: I,
394 ) -> Result<(), SynthesisError>
395 where
396 I: Iterator<Item = (B, &'a TEProjective<P>)>,
397 B: Borrow<Boolean<<P::BaseField as Field>::BasePrimeField>>,
398 {
399 let scalar_bits_with_base_powers = scalar_bits_with_base_powers
400 .map(|(bit, base)| (bit.borrow().clone(), (*base).into()))
401 .collect::<Vec<(_, TEProjective<P>)>>();
402 let zero = TEProjective::zero();
403 for bits_base_powers in scalar_bits_with_base_powers.chunks(2) {
404 if bits_base_powers.len() == 2 {
405 let bits = [bits_base_powers[0].0.clone(), bits_base_powers[1].0.clone()];
406 let base_powers = [&bits_base_powers[0].1, &bits_base_powers[1].1];
407
408 let mut table = [
409 zero,
410 *base_powers[0],
411 *base_powers[1],
412 *base_powers[0] + base_powers[1],
413 ];
414
415 TEProjective::batch_normalization(&mut table);
416 let x_s = [table[0].x, table[1].x, table[2].x, table[3].x];
417 let y_s = [table[0].y, table[1].y, table[2].y, table[3].y];
418
419 let x = F::two_bit_lookup(&bits, &x_s)?;
420 let y = F::two_bit_lookup(&bits, &y_s)?;
421 *self += Self::new(x, y);
422 } else if bits_base_powers.len() == 1 {
423 let bit = bits_base_powers[0].0.clone();
424 let base_power = bits_base_powers[0].1;
425 let new_encoded = &*self + base_power;
426 *self = bit.select(&new_encoded, &self)?;
427 }
428 }
429
430 Ok(())
431 }
432
433 fn precomputed_base_3_bit_signed_digit_scalar_mul<'a, I, J, B>(
434 bases: &[B],
435 scalars: &[J],
436 ) -> Result<Self, SynthesisError>
437 where
438 I: Borrow<[Boolean<<P::BaseField as Field>::BasePrimeField>]>,
439 J: Borrow<[I]>,
440 B: Borrow<[TEProjective<P>]>,
441 {
442 const CHUNK_SIZE: usize = 3;
443 let mut ed_result: Option<AffineVar<P, F>> = None;
444 let mut result: Option<MontgomeryAffineVar<P, F>> = None;
445
446 let mut process_segment_result = |result: &MontgomeryAffineVar<P, F>| {
447 let sgmt_result = result.into_edwards()?;
448 ed_result = match ed_result.as_ref() {
449 None => Some(sgmt_result),
450 Some(r) => Some(sgmt_result + r),
451 };
452 Ok::<(), SynthesisError>(())
453 };
454
455 // Compute ∏(h_i^{m_i}) for all i.
456 for (segment_bits_chunks, segment_powers) in scalars.iter().zip(bases) {
457 for (bits, base_power) in segment_bits_chunks
458 .borrow()
459 .iter()
460 .zip(segment_powers.borrow())
461 {
462 let base_power = base_power.borrow();
463 let mut acc_power = *base_power;
464 let mut coords = vec![];
465 for _ in 0..4 {
466 coords.push(acc_power);
467 acc_power += base_power;
468 }
469
470 let bits = bits.borrow().to_bits_le()?;
471 if bits.len() != CHUNK_SIZE {
472 return Err(SynthesisError::Unsatisfiable);
473 }
474
475 let coords = coords
476 .iter()
477 .map(|p| MontgomeryAffineVar::from_edwards_to_coords(&p.into_affine()))
478 .collect::<Result<Vec<_>, _>>()?;
479
480 let x_coeffs = coords.iter().map(|p| p.0).collect::<Vec<_>>();
481 let y_coeffs = coords.iter().map(|p| p.1).collect::<Vec<_>>();
482
483 let precomp = bits[0].and(&bits[1])?;
484
485 let x = F::zero()
486 + x_coeffs[0]
487 + F::from(bits[0].clone()) * (x_coeffs[1] - &x_coeffs[0])
488 + F::from(bits[1].clone()) * (x_coeffs[2] - &x_coeffs[0])
489 + F::from(precomp.clone())
490 * (x_coeffs[3] - &x_coeffs[2] - &x_coeffs[1] + &x_coeffs[0]);
491
492 let y = F::three_bit_cond_neg_lookup(&bits, &precomp, &y_coeffs)?;
493
494 let tmp = MontgomeryAffineVar::new(x, y);
495 result = match result.as_ref() {
496 None => Some(tmp),
497 Some(r) => Some(tmp + r),
498 };
499 }
500
501 process_segment_result(&result.unwrap())?;
502 result = None;
503 }
504 if result.is_some() {
505 process_segment_result(&result.unwrap())?;
506 }
507 Ok(ed_result.unwrap())
508 }
509}
510
511impl<P, F> AllocVar<TEProjective<P>, <P::BaseField as Field>::BasePrimeField> for AffineVar<P, F>
512where
513 P: TEModelParameters,
514 F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>
515 + TwoBitLookupGadget<<P::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>
516 + ThreeBitCondNegLookupGadget<
517 <P::BaseField as Field>::BasePrimeField,
518 TableConstant = P::BaseField,
519 >,
520 for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>,
521{
522 fn new_variable<Point: Borrow<TEProjective<P>>>(
523 cs: impl Into<Namespace<<P::BaseField as Field>::BasePrimeField>>,
524 f: impl FnOnce() -> Result<Point, SynthesisError>,
525 mode: AllocationMode,
526 ) -> Result<Self, SynthesisError> {
527 let ns = cs.into();
528 let cs = ns.cs();
529 let f = || Ok(*f()?.borrow());
530 match mode {
531 AllocationMode::Constant => Self::new_variable_omit_prime_order_check(cs, f, mode),
532 AllocationMode::Input => Self::new_variable_omit_prime_order_check(cs, f, mode),
533 AllocationMode::Witness => {
534 // if cofactor.is_even():
535 // divide until you've removed all even factors
536 // else:
537 // just directly use double and add.
538 let mut power_of_2: u32 = 0;
539 let mut cofactor = P::COFACTOR.to_vec();
540 while cofactor[0] % 2 == 0 {
541 div2(&mut cofactor);
542 power_of_2 += 1;
543 }
544
545 let cofactor_weight = BitIteratorBE::new(cofactor.as_slice())
546 .filter(|b| *b)
547 .count();
548 let modulus_minus_1 = (-P::ScalarField::one()).into_repr(); // r - 1
549 let modulus_minus_1_weight =
550 BitIteratorBE::new(modulus_minus_1).filter(|b| *b).count();
551
552 // We pick the most efficient method of performing the prime order check:
553 // If the cofactor has lower hamming weight than the scalar field's modulus,
554 // we first multiply by the inverse of the cofactor, and then, after allocating,
555 // multiply by the cofactor. This ensures the resulting point has no cofactors
556 //
557 // Else, we multiply by the scalar field's modulus and ensure that the result
558 // equals the identity.
559
560 let (mut ge, iter) = if cofactor_weight < modulus_minus_1_weight {
561 let ge = Self::new_variable_omit_prime_order_check(
562 cs.ns("Witness without subgroup check with cofactor mul"),
563 || f().map(|g| g.borrow().into_affine().mul_by_cofactor_inv().into()),
564 mode,
565 )?;
566 (
567 ge,
568 BitIteratorBE::without_leading_zeros(cofactor.as_slice()),
569 )
570 } else {
571 let ge = Self::new_variable_omit_prime_order_check(
572 cs.ns("Witness without subgroup check with `r` check"),
573 || {
574 f().map(|g| {
575 let g = g.into_affine();
576 let mut power_of_two = P::ScalarField::one().into_repr();
577 power_of_two.muln(power_of_2);
578 let power_of_two_inv = P::ScalarField::from_repr(power_of_two)
579 .and_then(|n| n.inverse())
580 .unwrap();
581 g.mul(power_of_two_inv)
582 })
583 },
584 mode,
585 )?;
586
587 (
588 ge,
589 BitIteratorBE::without_leading_zeros(modulus_minus_1.as_ref()),
590 )
591 };
592 // Remove the even part of the cofactor
593 for _ in 0..power_of_2 {
594 ge.double_in_place()?;
595 }
596
597 let mut result = Self::zero();
598 for b in iter {
599 result.double_in_place()?;
600 if b {
601 result += ≥
602 }
603 }
604 if cofactor_weight < modulus_minus_1_weight {
605 Ok(result)
606 } else {
607 ge.enforce_equal(&ge)?;
608 Ok(ge)
609 }
610 }
611 }
612 }
613}
614
615impl<P, F> AllocVar<TEAffine<P>, <P::BaseField as Field>::BasePrimeField> for AffineVar<P, F>
616where
617 P: TEModelParameters,
618 F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>
619 + TwoBitLookupGadget<<P::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>
620 + ThreeBitCondNegLookupGadget<
621 <P::BaseField as Field>::BasePrimeField,
622 TableConstant = P::BaseField,
623 >,
624 for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>,
625{
626 fn new_variable<Point: Borrow<TEAffine<P>>>(
627 cs: impl Into<Namespace<<P::BaseField as Field>::BasePrimeField>>,
628 f: impl FnOnce() -> Result<Point, SynthesisError>,
629 mode: AllocationMode,
630 ) -> Result<Self, SynthesisError> {
631 Self::new_variable(cs, || f().map(|b| b.borrow().into_projective()), mode)
632 }
633}
634
635#[inline]
636fn div2(limbs: &mut [u64]) {
637 let mut t = 0;
638 for i in limbs.iter_mut().rev() {
639 let t2 = *i << 63;
640 *i >>= 1;
641 *i |= t;
642 t = t2;
643 }
644}
645
646impl_bounded_ops!(
647 AffineVar<P, F>,
648 TEProjective<P>,
649 Add,
650 add,
651 AddAssign,
652 add_assign,
653 |this: &'a AffineVar<P, F>, other: &'a AffineVar<P, F>| {
654 if let Some(cs) = [this, other].cs() {
655 let a = P::COEFF_A;
656 let d = P::COEFF_D;
657
658 // Compute U = (x1 + y1) * (x2 + y2)
659 let u1 = (&this.x * -a) + &this.y;
660 let u2 = &other.x + &other.y;
661
662 let u = u1 * &u2;
663
664 // Compute v0 = x1 * y2
665 let v0 = &other.y * &this.x;
666
667 // Compute v1 = x2 * y1
668 let v1 = &other.x * &this.y;
669
670 // Compute C = d*v0*v1
671 let v2 = &v0 * &v1 * d;
672
673 // Compute x3 = (v0 + v1) / (1 + v2)
674 let x3 = F::new_witness(cs.ns("x3"), || {
675 let t0 = v0.value()? + &v1.value()?;
676 let t1 = P::BaseField::one() + &v2.value()?;
677 Ok(t0 * &t1.inverse().ok_or(SynthesisError::DivisionByZero)?)
678 }).unwrap();
679
680 let v2_plus_one = &v2 + P::BaseField::one();
681 let v0_plus_v1 = &v0 + &v1;
682 x3.mul_equals(&v2_plus_one, &v0_plus_v1).unwrap();
683
684 // Compute y3 = (U + a * v0 - v1) / (1 - v2)
685 let y3 = F::new_witness(cs.ns("y3"), || {
686 let t0 = u.value()? + &(a * &v0.value()?) - &v1.value()?;
687 let t1 = P::BaseField::one() - &v2.value()?;
688 Ok(t0 * &t1.inverse().ok_or(SynthesisError::DivisionByZero)?)
689 }).unwrap();
690
691 let one_minus_v2 = (&v2 - P::BaseField::one()).negate().unwrap();
692 let a_v0 = &v0 * a;
693 let u_plus_a_v0_minus_v1 = &u + &a_v0 - &v1;
694
695 y3.mul_equals(&one_minus_v2, &u_plus_a_v0_minus_v1).unwrap();
696
697 AffineVar::new(x3, y3)
698 } else {
699 assert!(this.is_constant() && other.is_constant());
700 AffineVar::constant(this.value().unwrap() + &other.value().unwrap())
701 }
702 },
703 |this: &'a AffineVar<P, F>, other: TEProjective<P>| this + AffineVar::constant(other),
704 (
705 F :FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>
706 + TwoBitLookupGadget<<P::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>
707 + ThreeBitCondNegLookupGadget<<P::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>,
708 P: TEModelParameters,
709 ),
710 for <'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,
711);
712
713impl_bounded_ops!(
714 AffineVar<P, F>,
715 TEProjective<P>,
716 Sub,
717 sub,
718 SubAssign,
719 sub_assign,
720 |this: &'a AffineVar<P, F>, other: &'a AffineVar<P, F>| this + other.negate().unwrap(),
721 |this: &'a AffineVar<P, F>, other: TEProjective<P>| this - AffineVar::constant(other),
722 (
723 F :FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>
724 + TwoBitLookupGadget<<P::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>
725 + ThreeBitCondNegLookupGadget<<P::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>,
726 P: TEModelParameters,
727 ),
728 for <'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>
729);
730
731impl<'a, P, F> GroupOpsBounds<'a, TEProjective<P>, AffineVar<P, F>> for AffineVar<P, F>
732where
733 P: TEModelParameters,
734 F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>
735 + TwoBitLookupGadget<<P::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>
736 + ThreeBitCondNegLookupGadget<
737 <P::BaseField as Field>::BasePrimeField,
738 TableConstant = P::BaseField,
739 >,
740 for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,
741{
742}
743
744impl<'a, P, F> GroupOpsBounds<'a, TEProjective<P>, AffineVar<P, F>> for &'a AffineVar<P, F>
745where
746 P: TEModelParameters,
747 F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>
748 + TwoBitLookupGadget<<P::BaseField as Field>::BasePrimeField, TableConstant = P::BaseField>
749 + ThreeBitCondNegLookupGadget<
750 <P::BaseField as Field>::BasePrimeField,
751 TableConstant = P::BaseField,
752 >,
753 for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,
754{
755}
756
757impl<P, F> CondSelectGadget<<P::BaseField as Field>::BasePrimeField> for AffineVar<P, F>
758where
759 P: TEModelParameters,
760 F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>,
761 for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,
762{
763 #[inline]
764 fn conditionally_select(
765 cond: &Boolean<<P::BaseField as Field>::BasePrimeField>,
766 true_value: &Self,
767 false_value: &Self,
768 ) -> Result<Self, SynthesisError> {
769 let x = cond.select(&true_value.x, &false_value.x)?;
770 let y = cond.select(&true_value.y, &false_value.y)?;
771
772 Ok(Self::new(x, y))
773 }
774}
775
776impl<P, F> EqGadget<<P::BaseField as Field>::BasePrimeField> for AffineVar<P, F>
777where
778 P: TEModelParameters,
779 F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>,
780 for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,
781{
782 fn is_eq(
783 &self,
784 other: &Self,
785 ) -> Result<Boolean<<P::BaseField as Field>::BasePrimeField>, SynthesisError> {
786 let x_equal = self.x.is_eq(&other.x)?;
787 let y_equal = self.y.is_eq(&other.y)?;
788 x_equal.and(&y_equal)
789 }
790
791 #[inline]
792 fn conditional_enforce_equal(
793 &self,
794 other: &Self,
795 condition: &Boolean<<P::BaseField as Field>::BasePrimeField>,
796 ) -> Result<(), SynthesisError> {
797 self.x.conditional_enforce_equal(&other.x, condition)?;
798 self.y.conditional_enforce_equal(&other.y, condition)?;
799 Ok(())
800 }
801
802 #[inline]
803 fn conditional_enforce_not_equal(
804 &self,
805 other: &Self,
806 condition: &Boolean<<P::BaseField as Field>::BasePrimeField>,
807 ) -> Result<(), SynthesisError> {
808 self.is_eq(other)?
809 .and(condition)?
810 .enforce_equal(&Boolean::Constant(false))
811 }
812}
813
814impl<P, F> ToBitsGadget<<P::BaseField as Field>::BasePrimeField> for AffineVar<P, F>
815where
816 P: TEModelParameters,
817 F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>,
818 for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,
819{
820 fn to_bits_le(
821 &self,
822 ) -> Result<Vec<Boolean<<P::BaseField as Field>::BasePrimeField>>, SynthesisError> {
823 let mut x_bits = self.x.to_bits_le()?;
824 let y_bits = self.y.to_bits_le()?;
825 x_bits.extend_from_slice(&y_bits);
826 Ok(x_bits)
827 }
828
829 fn to_non_unique_bits_le(
830 &self,
831 ) -> Result<Vec<Boolean<<P::BaseField as Field>::BasePrimeField>>, SynthesisError> {
832 let mut x_bits = self.x.to_non_unique_bits_le()?;
833 let y_bits = self.y.to_non_unique_bits_le()?;
834 x_bits.extend_from_slice(&y_bits);
835
836 Ok(x_bits)
837 }
838}
839
840impl<P, F> ToBytesGadget<<P::BaseField as Field>::BasePrimeField> for AffineVar<P, F>
841where
842 P: TEModelParameters,
843 F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>,
844 for<'b> &'b F: FieldOpsBounds<'b, P::BaseField, F>,
845{
846 fn to_bytes(
847 &self,
848 ) -> Result<Vec<UInt8<<P::BaseField as Field>::BasePrimeField>>, SynthesisError> {
849 let mut x_bytes = self.x.to_bytes()?;
850 let y_bytes = self.y.to_bytes()?;
851 x_bytes.extend_from_slice(&y_bytes);
852 Ok(x_bytes)
853 }
854
855 fn to_non_unique_bytes(
856 &self,
857 ) -> Result<Vec<UInt8<<P::BaseField as Field>::BasePrimeField>>, SynthesisError> {
858 let mut x_bytes = self.x.to_non_unique_bytes()?;
859 let y_bytes = self.y.to_non_unique_bytes()?;
860 x_bytes.extend_from_slice(&y_bytes);
861
862 Ok(x_bytes)
863 }
864}
865
866#[cfg(test)]
867#[allow(dead_code)]
868pub(crate) fn test<P, GG>() -> Result<(), SynthesisError>
869where
870 P: TEModelParameters,
871 GG: CurveVar<TEProjective<P>, <P::BaseField as Field>::BasePrimeField>,
872 for<'a> &'a GG: GroupOpsBounds<'a, TEProjective<P>, GG>,
873{
874 use crate::prelude::*;
875 use algebra::{test_rng, BitIteratorLE, Group, UniformRand};
876 use r1cs_core::ConstraintSystem;
877
878 crate::groups::test::group_test::<TEProjective<P>, _, GG>()?;
879
880 let mut rng = test_rng();
881
882 let cs = ConstraintSystem::<<P::BaseField as Field>::BasePrimeField>::new_ref();
883
884 let a = TEProjective::<P>::rand(&mut rng);
885 let b = TEProjective::<P>::rand(&mut rng);
886 let a_affine = a.into_affine();
887 let b_affine = b.into_affine();
888
889 println!("Allocating things");
890 let ns = cs.ns("allocating variables");
891 println!("{:?}", cs.current_namespace());
892 let mut gadget_a = GG::new_witness(cs.ns("a"), || Ok(a))?;
893 let gadget_b = GG::new_witness(cs.ns("b"), || Ok(b))?;
894 println!("{:?}", cs.current_namespace());
895 ns.leave_namespace();
896 println!("Done Allocating things");
897 assert_eq!(gadget_a.value()?.into_affine().x, a_affine.x);
898 assert_eq!(gadget_a.value()?.into_affine().y, a_affine.y);
899 assert_eq!(gadget_b.value()?.into_affine().x, b_affine.x);
900 assert_eq!(gadget_b.value()?.into_affine().y, b_affine.y);
901 assert_eq!(cs.which_is_unsatisfied(), None);
902
903 println!("Checking addition");
904 // Check addition
905 let ab = a + &b;
906 let ab_affine = ab.into_affine();
907 let gadget_ab = &gadget_a + &gadget_b;
908 let gadget_ba = &gadget_b + &gadget_a;
909 gadget_ba.enforce_equal(&gadget_ab)?;
910
911 let ab_val = gadget_ab.value()?.into_affine();
912 assert_eq!(ab_val, ab_affine, "Result of addition is unequal");
913 assert!(cs.is_satisfied().unwrap());
914 println!("Done checking addition");
915
916 println!("Checking doubling");
917 // Check doubling
918 let aa = Group::double(&a);
919 let aa_affine = aa.into_affine();
920 gadget_a.double_in_place()?;
921 let aa_val = gadget_a.value()?.into_affine();
922 assert_eq!(
923 aa_val, aa_affine,
924 "Gadget and native values are unequal after double."
925 );
926 assert!(cs.is_satisfied().unwrap());
927 println!("Done checking doubling");
928
929 println!("Checking mul_bits");
930 // Check mul_bits
931 let scalar = P::ScalarField::rand(&mut rng);
932 let native_result = AffineCurve::mul(&aa.into_affine(), scalar);
933 let native_result = native_result.into_affine();
934
935 let scalar: Vec<bool> = BitIteratorLE::new(scalar.into_repr()).collect();
936 let input: Vec<Boolean<_>> = Vec::new_witness(cs.ns("bits"), || Ok(scalar)).unwrap();
937 let result = gadget_a.scalar_mul_le(input.iter())?;
938 let result_val = result.value()?.into_affine();
939 assert_eq!(
940 result_val, native_result,
941 "gadget & native values are diff. after scalar mul"
942 );
943 assert!(cs.is_satisfied().unwrap());
944 println!("Done checking mul_bits");
945
946 if !cs.is_satisfied().unwrap() {
947 println!("Not satisfied");
948 println!("{:?}", cs.which_is_unsatisfied().unwrap());
949 }
950
951 assert!(cs.is_satisfied().unwrap());
952 Ok(())
953}