arnaucube
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sonobe/folding-schemes/src/commitment/ipa.rs
folding-schemes/src/commitment/ipa.rsRaw
  1/// IPA implements the modified Inner Product Argument described in
  2/// [Halo](https://eprint.iacr.org/2019/1021.pdf). The variable names used follow the paper
  3/// notation in order to make it more readable.
  4///
  5/// The implementation does the following optimizations in order to reduce the amount of
  6/// constraints in the circuit:
  7/// i. <s, b> computation is done in log time following a modification of the equation 3 in section
  8/// 3.2 from the paper.
  9/// ii. s computation is done in 2^{k+1}-2 instead of k*2^k.
 10use ark_ec::{AffineRepr, CurveGroup};
 11use ark_ff::{Field, PrimeField};
 12use ark_r1cs_std::{
 13    alloc::{AllocVar, AllocationMode},
 14    boolean::Boolean,
 15    fields::{nonnative::NonNativeFieldVar, FieldVar},
 16    prelude::CurveVar,
 17    ToBitsGadget,
 18};
 19use ark_relations::r1cs::{Namespace, SynthesisError};
 20use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
 21use ark_std::{cfg_iter, rand::RngCore, UniformRand, Zero};
 22use core::{borrow::Borrow, marker::PhantomData};
 23use rayon::iter::{IndexedParallelIterator, IntoParallelRefIterator, ParallelIterator};
 24
 25use super::{pedersen::Params as PedersenParams, CommitmentScheme};
 26use crate::transcript::Transcript;
 27use crate::utils::{
 28    powers_of,
 29    vec::{vec_add, vec_scalar_mul},
 30};
 31use crate::Error;
 32
 33#[derive(Debug, Clone, Eq, PartialEq, CanonicalSerialize, CanonicalDeserialize)]
 34pub struct Proof<C: CurveGroup> {
 35    a: C::ScalarField,
 36    l: Vec<C::ScalarField>,
 37    r: Vec<C::ScalarField>,
 38    L: Vec<C>,
 39    R: Vec<C>,
 40}
 41
 42/// IPA implements the Inner Product Argument protocol following the CommitmentScheme trait. The
 43/// `H` parameter indicates if to use the commitment in hiding mode or not.
 44#[derive(Debug, Clone, Eq, PartialEq)]
 45pub struct IPA<C: CurveGroup, const H: bool = false> {
 46    _c: PhantomData<C>,
 47}
 48
 49/// Implements the CommitmentScheme trait for IPA
 50impl<C: CurveGroup, const H: bool> CommitmentScheme<C, H> for IPA<C, H> {
 51    type ProverParams = PedersenParams<C>;
 52    type VerifierParams = PedersenParams<C>;
 53    type Proof = (Proof<C>, C::ScalarField, C::ScalarField); // (proof, v=p(x), r=blinding factor)
 54    type ProverChallenge = (C::ScalarField, C, Vec<C::ScalarField>);
 55    type Challenge = (C::ScalarField, C, Vec<C::ScalarField>);
 56
 57    fn is_hiding() -> bool {
 58        if H {
 59            return true;
 60        }
 61        false
 62    }
 63
 64    fn setup(
 65        mut rng: impl RngCore,
 66        len: usize,
 67    ) -> Result<(Self::ProverParams, Self::VerifierParams), Error> {
 68        let generators: Vec<C::Affine> = std::iter::repeat_with(|| C::Affine::rand(&mut rng))
 69            .take(len.next_power_of_two())
 70            .collect();
 71        let p = PedersenParams::<C> {
 72            h: C::rand(&mut rng),
 73            generators,
 74        };
 75        Ok((p.clone(), p))
 76    }
 77
 78    fn commit(
 79        params: &PedersenParams<C>,
 80        a: &[C::ScalarField],
 81        r: &C::ScalarField, // blinding factor
 82    ) -> Result<C, Error> {
 83        if params.generators.len() < a.len() {
 84            return Err(Error::PedersenParamsLen(params.generators.len(), a.len()));
 85        }
 86        if !H && (!r.is_zero()) {
 87            return Err(Error::BlindingNotZero);
 88        }
 89
 90        // h⋅r + <g, a>
 91        // use msm_unchecked because we already ensured at the if that lengths match
 92        if !H {
 93            return Ok(C::msm_unchecked(&params.generators[..a.len()], a));
 94        }
 95        Ok(params.h.mul(r) + C::msm_unchecked(&params.generators[..a.len()], a))
 96    }
 97
 98    fn prove(
 99        params: &Self::ProverParams,
100        transcript: &mut impl Transcript<C::ScalarField>,
101        P: &C,                // commitment
102        a: &[C::ScalarField], // vector
103        blind: &C::ScalarField,
104        rng: Option<&mut dyn RngCore>,
105    ) -> Result<Self::Proof, Error> {
106        if !a.len().is_power_of_two() {
107            return Err(Error::NotPowerOfTwo("a".to_string(), a.len()));
108        }
109        if !H && (!blind.is_zero()) {
110            return Err(Error::BlindingNotZero);
111        }
112        let d = a.len();
113        let k = (f64::from(d as u32).log2()) as usize;
114
115        if params.generators.len() < a.len() {
116            return Err(Error::PedersenParamsLen(params.generators.len(), a.len()));
117        }
118        // blinding factors
119        let l: Vec<C::ScalarField>;
120        let r: Vec<C::ScalarField>;
121        if H {
122            let rng = rng.ok_or(Error::MissingRandomness)?;
123            l = std::iter::repeat_with(|| C::ScalarField::rand(rng))
124                .take(k)
125                .collect();
126            r = std::iter::repeat_with(|| C::ScalarField::rand(rng))
127                .take(k)
128                .collect();
129        } else {
130            l = vec![];
131            r = vec![];
132        }
133
134        transcript.absorb_nonnative(P);
135        let x = transcript.get_challenge(); // challenge value at which we evaluate
136        let s = transcript.get_challenge();
137        let U = C::generator().mul(s);
138
139        let mut a = a.to_owned();
140        let mut b = powers_of(x, d);
141        let v = inner_prod(&a, &b)?;
142
143        let mut G = params.generators.clone();
144
145        let mut L: Vec<C> = vec![C::zero(); k];
146        let mut R: Vec<C> = vec![C::zero(); k];
147
148        // u challenges
149        let mut u: Vec<C::ScalarField> = vec![C::ScalarField::zero(); k];
150        for j in (0..k).rev() {
151            let m = a.len() / 2;
152
153            if H {
154                L[j] = C::msm_unchecked(&G[m..], &a[..m])
155                    + params.h.mul(l[j])
156                    + U.mul(inner_prod(&a[..m], &b[m..])?);
157                R[j] = C::msm_unchecked(&G[..m], &a[m..])
158                    + params.h.mul(r[j])
159                    + U.mul(inner_prod(&a[m..], &b[..m])?);
160            } else {
161                L[j] = C::msm_unchecked(&G[m..], &a[..m]) + U.mul(inner_prod(&a[..m], &b[m..])?);
162                R[j] = C::msm_unchecked(&G[..m], &a[m..]) + U.mul(inner_prod(&a[m..], &b[..m])?);
163            }
164            // get challenge for the j-th round
165            transcript.absorb_nonnative(&L[j]);
166            transcript.absorb_nonnative(&R[j]);
167            u[j] = transcript.get_challenge();
168
169            let uj = u[j];
170            let uj_inv = u[j]
171                .inverse()
172                .ok_or(Error::Other("error on computing inverse".to_string()))?;
173
174            // a_hi * uj^-1 + a_lo * uj
175            a = vec_add(
176                &vec_scalar_mul(&a[..m], &uj),
177                &vec_scalar_mul(&a[m..], &uj_inv),
178            )?;
179            // b_lo * uj^-1 + b_hi * uj
180            b = vec_add(
181                &vec_scalar_mul(&b[..m], &uj_inv),
182                &vec_scalar_mul(&b[m..], &uj),
183            )?;
184            // G_lo * uj^-1 + G_hi * uj
185            G = cfg_iter!(G[..m])
186                .map(|e| e.into_group().mul(uj_inv))
187                .zip(cfg_iter!(G[m..]).map(|e| e.into_group().mul(uj)))
188                .map(|(a, b)| (a + b).into_affine())
189                .collect::<Vec<C::Affine>>();
190        }
191
192        if a.len() != 1 {
193            return Err(Error::NotExpectedLength(a.len(), 1));
194        }
195        if b.len() != 1 {
196            return Err(Error::NotExpectedLength(b.len(), 1));
197        }
198        if G.len() != 1 {
199            return Err(Error::NotExpectedLength(G.len(), 1));
200        }
201
202        Ok((
203            Proof {
204                a: a[0],
205                l: l.clone(),
206                r: r.clone(),
207                L,
208                R,
209            },
210            v,      // evaluation at challenge, v=p(x)
211            *blind, // blind factor
212        ))
213    }
214
215    fn prove_with_challenge(
216        _params: &Self::ProverParams,
217        _challenge: Self::ProverChallenge,
218        _a: &[C::ScalarField], // vector
219        _blind: &C::ScalarField,
220        _rng: Option<&mut dyn RngCore>,
221    ) -> Result<Self::Proof, Error> {
222        // not supported because the prover logic computes challenges as it advances on the logic
223        Err(Error::NotSupported("IPA::prove_with_challenge".to_string()))
224    }
225
226    fn verify(
227        params: &Self::VerifierParams,
228        transcript: &mut impl Transcript<C::ScalarField>,
229        P: &C, // commitment
230        proof: &Self::Proof,
231    ) -> Result<(), Error> {
232        let (p, _r) = (proof.0.clone(), proof.1);
233        let k = p.L.len();
234
235        transcript.absorb_nonnative(P);
236        let x = transcript.get_challenge(); // challenge value at which we evaluate
237        let s = transcript.get_challenge();
238        let U = C::generator().mul(s);
239        let mut u: Vec<C::ScalarField> = vec![C::ScalarField::zero(); k];
240        for i in (0..k).rev() {
241            transcript.absorb_nonnative(&p.L[i]);
242            transcript.absorb_nonnative(&p.R[i]);
243            u[i] = transcript.get_challenge();
244        }
245        let challenge = (x, U, u);
246
247        Self::verify_with_challenge(params, challenge, P, proof)
248    }
249
250    fn verify_with_challenge(
251        params: &Self::VerifierParams,
252        challenge: Self::Challenge,
253        P: &C, // commitment
254        proof: &Self::Proof,
255    ) -> Result<(), Error> {
256        let (p, v, r) = (proof.0.clone(), proof.1, proof.2);
257        let (x, U, u) = challenge;
258
259        let k = p.L.len();
260        if p.R.len() != k {
261            return Err(Error::CommitmentVerificationFail);
262        }
263        if !H && (!r.is_zero()) {
264            return Err(Error::BlindingNotZero);
265        }
266        if !H && (!p.l.is_empty() || !p.r.is_empty()) {
267            return Err(Error::CommitmentVerificationFail);
268        }
269        if H && (p.l.len() != k || p.r.len() != k) {
270            return Err(Error::CommitmentVerificationFail);
271        }
272
273        let P = *P + U.mul(v); // where v=p(x)
274
275        let mut q_0 = P;
276        let mut r = r;
277
278        // compute u[i]^-1 once
279        let mut u_invs = vec![C::ScalarField::zero(); u.len()];
280        for (j, u_j) in u.iter().enumerate() {
281            u_invs[j] = u_j
282                .inverse()
283                .ok_or(Error::Other("error on computing inverse".to_string()))?;
284        }
285
286        // compute b & G from s
287        let s = build_s(&u, &u_invs, k)?;
288        // b = <s, b_vec> = <s, [1, x, x^2, ..., x^d-1]>
289        let b = s_b_inner(&u, &x)?;
290        let d: usize = 2_u64.pow(k as u32) as usize;
291        if params.generators.len() < d {
292            return Err(Error::PedersenParamsLen(params.generators.len(), d));
293        }
294        let G = C::msm_unchecked(&params.generators, &s);
295
296        for (j, u_j) in u.iter().enumerate() {
297            let uj2 = u_j.square();
298            let uj_inv2 = u_invs[j].square();
299
300            q_0 = q_0 + p.L[j].mul(uj2) + p.R[j].mul(uj_inv2);
301            if H {
302                r = r + p.l[j] * uj2 + p.r[j] * uj_inv2;
303            }
304        }
305
306        let q_1 = if H {
307            G.mul(p.a) + params.h.mul(r) + U.mul(p.a * b)
308        } else {
309            G.mul(p.a) + U.mul(p.a * b)
310        };
311
312        if q_0 != q_1 {
313            return Err(Error::CommitmentVerificationFail);
314        }
315        Ok(())
316    }
317}
318
319/// Computes s such that
320/// s = (
321///   u₁⁻¹ u₂⁻¹ … uₖ⁻¹,
322///   u₁   u₂⁻¹ … uₖ⁻¹,
323///   u₁⁻¹ u₂   … uₖ⁻¹,
324///   u₁   u₂   … uₖ⁻¹,
325///   ⋮    ⋮      ⋮
326///   u₁   u₂   … uₖ
327/// )
328/// Uses Halo2 approach computing $g(X) = \prod\limits_{i=0}^{k-1} (1 + u_{k - 1 - i} X^{2^i})$,
329/// taking 2^{k+1}-2.
330/// src: https://github.com/zcash/halo2/blob/81729eca91ba4755e247f49c3a72a4232864ec9e/halo2_proofs/src/poly/commitment/verifier.rs#L156
331fn build_s<F: PrimeField>(u: &[F], u_invs: &[F], k: usize) -> Result<Vec<F>, Error> {
332    let d: usize = 2_u64.pow(k as u32) as usize;
333    let mut s: Vec<F> = vec![F::one(); d];
334    for (len, (u_j, u_j_inv)) in u
335        .iter()
336        .zip(u_invs)
337        .enumerate()
338        .map(|(i, u_j)| (1 << i, u_j))
339    {
340        let (left, right) = s.split_at_mut(len);
341        let right = &mut right[0..len];
342        right.copy_from_slice(left);
343        for s in left {
344            *s *= u_j_inv;
345        }
346        for s in right {
347            *s *= u_j;
348        }
349    }
350    Ok(s)
351}
352
353/// Computes (in-circuit) s such that
354/// s = (
355///   u₁⁻¹ u₂⁻¹ … uₖ⁻¹,
356///   u₁   u₂⁻¹ … uₖ⁻¹,
357///   u₁⁻¹ u₂   … uₖ⁻¹,
358///   u₁   u₂   … uₖ⁻¹,
359///   ⋮    ⋮      ⋮
360///   u₁   u₂   … uₖ
361/// )
362/// Uses Halo2 approach computing $g(X) = \prod\limits_{i=0}^{k-1} (1 + u_{k - 1 - i} X^{2^i})$,
363/// taking 2^{k+1}-2.
364/// src: https://github.com/zcash/halo2/blob/81729eca91ba4755e247f49c3a72a4232864ec9e/halo2_proofs/src/poly/commitment/verifier.rs#L156
365fn build_s_gadget<F: PrimeField, CF: PrimeField>(
366    u: &[NonNativeFieldVar<F, CF>],
367    u_invs: &[NonNativeFieldVar<F, CF>],
368    k: usize,
369) -> Result<Vec<NonNativeFieldVar<F, CF>>, SynthesisError> {
370    let d: usize = 2_u64.pow(k as u32) as usize;
371    let mut s: Vec<NonNativeFieldVar<F, CF>> = vec![NonNativeFieldVar::one(); d];
372    for (len, (u_j, u_j_inv)) in u
373        .iter()
374        .zip(u_invs)
375        .enumerate()
376        .map(|(i, u_j)| (1 << i, u_j))
377    {
378        let (left, right) = s.split_at_mut(len);
379        let right = &mut right[0..len];
380        right.clone_from_slice(left);
381        for s in left {
382            *s *= u_j_inv;
383        }
384        for s in right {
385            *s *= u_j;
386        }
387    }
388    Ok(s)
389}
390
391fn inner_prod<F: PrimeField>(a: &[F], b: &[F]) -> Result<F, Error> {
392    if a.len() != b.len() {
393        return Err(Error::NotSameLength(
394            "a".to_string(),
395            a.len(),
396            "b".to_string(),
397            b.len(),
398        ));
399    }
400    let c = cfg_iter!(a)
401        .zip(cfg_iter!(b))
402        .map(|(a_i, b_i)| *a_i * b_i)
403        .sum();
404    Ok(c)
405}
406
407// g(x, u_1, u_2, ..., u_k) = <s, b>, naively takes linear, but can compute in log time through
408// g(x, u_1, u_2, ..., u_k) = \Prod u_i x^{2^i} + u_i^-1
409fn s_b_inner<F: PrimeField>(u: &[F], x: &F) -> Result<F, Error> {
410    let mut c: F = F::one();
411    let mut x_2_i = *x; // x_2_i is x^{2^i}, starting from x^{2^0}=x
412    for u_i in u.iter() {
413        c *= (*u_i * x_2_i)
414            + u_i
415                .inverse()
416                .ok_or(Error::Other("error on computing inverse".to_string()))?;
417        x_2_i *= x_2_i;
418    }
419    Ok(c)
420}
421
422// g(x, u_1, u_2, ..., u_k) = <s, b>, naively takes linear, but can compute in log time through
423// g(x, u_1, u_2, ..., u_k) = \Prod u_i x^{2^i} + u_i^-1
424fn s_b_inner_gadget<F: PrimeField, CF: PrimeField>(
425    u: &[NonNativeFieldVar<F, CF>],
426    x: &NonNativeFieldVar<F, CF>,
427) -> Result<NonNativeFieldVar<F, CF>, SynthesisError> {
428    let mut c: NonNativeFieldVar<F, CF> = NonNativeFieldVar::<F, CF>::one();
429    let mut x_2_i = x.clone(); // x_2_i is x^{2^i}, starting from x^{2^0}=x
430    for u_i in u.iter() {
431        c *= u_i.clone() * x_2_i.clone() + u_i.inverse()?;
432        x_2_i *= x_2_i.clone();
433    }
434    Ok(c)
435}
436
437pub type CF<C> = <<C as CurveGroup>::BaseField as Field>::BasePrimeField;
438
439pub struct ProofVar<C: CurveGroup, GC: CurveVar<C, CF<C>>> {
440    a: NonNativeFieldVar<C::ScalarField, CF<C>>,
441    l: Vec<NonNativeFieldVar<C::ScalarField, CF<C>>>,
442    r: Vec<NonNativeFieldVar<C::ScalarField, CF<C>>>,
443    L: Vec<GC>,
444    R: Vec<GC>,
445}
446impl<C, GC> AllocVar<Proof<C>, CF<C>> for ProofVar<C, GC>
447where
448    C: CurveGroup,
449    GC: CurveVar<C, CF<C>>,
450    <C as ark_ec::CurveGroup>::BaseField: PrimeField,
451{
452    fn new_variable<T: Borrow<Proof<C>>>(
453        cs: impl Into<Namespace<CF<C>>>,
454        f: impl FnOnce() -> Result<T, SynthesisError>,
455        mode: AllocationMode,
456    ) -> Result<Self, SynthesisError> {
457        f().and_then(|val| {
458            let cs = cs.into();
459
460            let a = NonNativeFieldVar::<C::ScalarField, CF<C>>::new_variable(
461                cs.clone(),
462                || Ok(val.borrow().a),
463                mode,
464            )?;
465            let l: Vec<NonNativeFieldVar<C::ScalarField, CF<C>>> =
466                Vec::new_variable(cs.clone(), || Ok(val.borrow().l.clone()), mode)?;
467            let r: Vec<NonNativeFieldVar<C::ScalarField, CF<C>>> =
468                Vec::new_variable(cs.clone(), || Ok(val.borrow().r.clone()), mode)?;
469            let L: Vec<GC> = Vec::new_variable(cs.clone(), || Ok(val.borrow().L.clone()), mode)?;
470            let R: Vec<GC> = Vec::new_variable(cs.clone(), || Ok(val.borrow().R.clone()), mode)?;
471
472            Ok(Self { a, l, r, L, R })
473        })
474    }
475}
476
477/// IPAGadget implements the circuit that verifies an IPA Proof. The `H` parameter indicates if to
478/// use the commitment in hiding mode or not, reducing a bit the number of constraints needed in
479/// the later case.
480pub struct IPAGadget<C, GC, const H: bool = false>
481where
482    C: CurveGroup,
483    GC: CurveVar<C, CF<C>>,
484{
485    _cf: PhantomData<CF<C>>,
486    _c: PhantomData<C>,
487    _gc: PhantomData<GC>,
488}
489
490impl<C, GC, const H: bool> IPAGadget<C, GC, H>
491where
492    C: CurveGroup,
493    GC: CurveVar<C, CF<C>>,
494{
495    /// Verify the IPA opening proof, K=log2(d), where d is the degree of the committed polynomial,
496    /// and H indicates if the commitment is in hiding mode and thus uses blinding factors, if not,
497    /// there are some constraints saved.
498    #[allow(clippy::too_many_arguments)]
499    pub fn verify<const K: usize>(
500        g: &[GC],                                     // params.generators
501        h: &GC,                                       // params.h
502        x: &NonNativeFieldVar<C::ScalarField, CF<C>>, // evaluation point, challenge
503        v: &NonNativeFieldVar<C::ScalarField, CF<C>>, // value at evaluation point
504        P: &GC,                                       // commitment
505        p: &ProofVar<C, GC>,
506        r: &NonNativeFieldVar<C::ScalarField, CF<C>>, // blinding factor
507        u: &[NonNativeFieldVar<C::ScalarField, CF<C>>; K], // challenges
508        U: &GC,                                       // challenge
509    ) -> Result<Boolean<CF<C>>, SynthesisError> {
510        if p.L.len() != K || p.R.len() != K {
511            return Err(SynthesisError::Unsatisfiable);
512        }
513
514        let P_ = U.scalar_mul_le(v.to_bits_le()?.iter())? + P;
515        let mut q_0 = P_;
516        let mut r = r.clone();
517
518        // compute u[i]^-1 once
519        let mut u_invs = vec![NonNativeFieldVar::<C::ScalarField, CF<C>>::zero(); u.len()];
520        for (j, u_j) in u.iter().enumerate() {
521            u_invs[j] = u_j.inverse()?;
522        }
523
524        // compute b & G from s
525        let s = build_s_gadget(u, &u_invs, K)?;
526        // b = <s, b_vec> = <s, [1, x, x^2, ..., x^K-1]>
527        let b = s_b_inner_gadget(u, x)?;
528        // ensure that generators.len() === s.len():
529        if g.len() < K {
530            return Err(SynthesisError::Unsatisfiable);
531        }
532
533        // msm: G=<G, s>
534        let mut G = GC::zero();
535        for (i, s_i) in s.iter().enumerate() {
536            G += g[i].scalar_mul_le(s_i.to_bits_le()?.iter())?;
537        }
538
539        for (j, u_j) in u.iter().enumerate() {
540            let uj2 = u_j.square()?;
541            let uj_inv2 = u_invs[j].square()?; // cheaper square than inversing the uj2
542
543            q_0 = q_0
544                + p.L[j].scalar_mul_le(uj2.to_bits_le()?.iter())?
545                + p.R[j].scalar_mul_le(uj_inv2.to_bits_le()?.iter())?;
546            if H {
547                r = r + &p.l[j] * &uj2 + &p.r[j] * &uj_inv2;
548            }
549        }
550
551        let q_1 = if H {
552            G.scalar_mul_le(p.a.to_bits_le()?.iter())?
553                + h.scalar_mul_le(r.to_bits_le()?.iter())?
554                + U.scalar_mul_le((p.a.clone() * b).to_bits_le()?.iter())?
555        } else {
556            G.scalar_mul_le(p.a.to_bits_le()?.iter())?
557                + U.scalar_mul_le((p.a.clone() * b).to_bits_le()?.iter())?
558        };
559        // q_0 == q_1
560        q_0.is_eq(&q_1)
561    }
562}
563
564#[cfg(test)]
565mod tests {
566    use ark_crypto_primitives::sponge::{poseidon::PoseidonSponge, CryptographicSponge};
567    use ark_ec::Group;
568    use ark_pallas::{constraints::GVar, Fq, Fr, Projective};
569    use ark_r1cs_std::eq::EqGadget;
570    use ark_relations::r1cs::ConstraintSystem;
571    use std::ops::Mul;
572
573    use super::*;
574    use crate::transcript::poseidon::poseidon_canonical_config;
575
576    #[test]
577    fn test_ipa() {
578        test_ipa_opt::<false>();
579        test_ipa_opt::<true>();
580    }
581    fn test_ipa_opt<const hiding: bool>() {
582        let mut rng = ark_std::test_rng();
583
584        const k: usize = 4;
585        const d: usize = 2_u64.pow(k as u32) as usize;
586
587        // setup params
588        let (params, _) = IPA::<Projective, hiding>::setup(&mut rng, d).unwrap();
589
590        let poseidon_config = poseidon_canonical_config::<Fr>();
591        // init Prover's transcript
592        let mut transcript_p = PoseidonSponge::<Fr>::new(&poseidon_config);
593        // init Verifier's transcript
594        let mut transcript_v = PoseidonSponge::<Fr>::new(&poseidon_config);
595
596        // a is the vector that we're committing
597        let a: Vec<Fr> = std::iter::repeat_with(|| Fr::rand(&mut rng))
598            .take(d)
599            .collect();
600        let r_blind: Fr = if hiding {
601            Fr::rand(&mut rng)
602        } else {
603            Fr::zero()
604        };
605        let cm = IPA::<Projective, hiding>::commit(&params, &a, &r_blind).unwrap();
606
607        let proof = IPA::<Projective, hiding>::prove(
608            &params,
609            &mut transcript_p,
610            &cm,
611            &a,
612            &r_blind,
613            Some(&mut rng),
614        )
615        .unwrap();
616
617        IPA::<Projective, hiding>::verify(&params, &mut transcript_v, &cm, &proof).unwrap();
618    }
619
620    #[test]
621    fn test_ipa_gadget() {
622        test_ipa_gadget_opt::<false>();
623        test_ipa_gadget_opt::<true>();
624    }
625    fn test_ipa_gadget_opt<const hiding: bool>() {
626        let mut rng = ark_std::test_rng();
627
628        const k: usize = 3;
629        const d: usize = 2_u64.pow(k as u32) as usize;
630
631        // setup params
632        let (params, _) = IPA::<Projective, hiding>::setup(&mut rng, d).unwrap();
633
634        let poseidon_config = poseidon_canonical_config::<Fr>();
635        // init Prover's transcript
636        let mut transcript_p = PoseidonSponge::<Fr>::new(&poseidon_config);
637        // init Verifier's transcript
638        let mut transcript_v = PoseidonSponge::<Fr>::new(&poseidon_config);
639
640        let mut a: Vec<Fr> = std::iter::repeat_with(|| Fr::rand(&mut rng))
641            .take(d / 2)
642            .collect();
643        a.extend(vec![Fr::zero(); d / 2]);
644        let r_blind: Fr = if hiding {
645            Fr::rand(&mut rng)
646        } else {
647            Fr::zero()
648        };
649        let cm = IPA::<Projective, hiding>::commit(&params, &a, &r_blind).unwrap();
650
651        let proof = IPA::<Projective, hiding>::prove(
652            &params,
653            &mut transcript_p,
654            &cm,
655            &a,
656            &r_blind,
657            Some(&mut rng),
658        )
659        .unwrap();
660
661        IPA::<Projective, hiding>::verify(&params, &mut transcript_v, &cm, &proof).unwrap();
662
663        // circuit
664        let cs = ConstraintSystem::<Fq>::new_ref();
665
666        let mut transcript_v = PoseidonSponge::<Fr>::new(&poseidon_config);
667        transcript_v.absorb_nonnative(&cm);
668        let challenge = transcript_v.get_challenge(); // challenge value at which we evaluate
669        let s = transcript_v.get_challenge();
670        let U = Projective::generator().mul(s);
671        let mut u: Vec<Fr> = vec![Fr::zero(); k];
672        for i in (0..k).rev() {
673            transcript_v.absorb_nonnative(&proof.0.L[i]);
674            transcript_v.absorb_nonnative(&proof.0.R[i]);
675            u[i] = transcript_v.get_challenge();
676        }
677
678        // prepare inputs
679        let gVar = Vec::<GVar>::new_constant(cs.clone(), params.generators).unwrap();
680        let hVar = GVar::new_constant(cs.clone(), params.h).unwrap();
681        let challengeVar =
682            NonNativeFieldVar::<Fr, Fq>::new_witness(cs.clone(), || Ok(challenge)).unwrap();
683        let vVar = NonNativeFieldVar::<Fr, Fq>::new_witness(cs.clone(), || Ok(proof.1)).unwrap();
684        let cmVar = GVar::new_witness(cs.clone(), || Ok(cm)).unwrap();
685        let proofVar =
686            ProofVar::<Projective, GVar>::new_witness(cs.clone(), || Ok(proof.0)).unwrap();
687        let r_blindVar =
688            NonNativeFieldVar::<Fr, Fq>::new_witness(cs.clone(), || Ok(r_blind)).unwrap();
689        let uVar_vec = Vec::<NonNativeFieldVar<Fr, Fq>>::new_witness(cs.clone(), || Ok(u)).unwrap();
690        let uVar: [NonNativeFieldVar<Fr, Fq>; k] = uVar_vec.try_into().unwrap();
691        let UVar = GVar::new_witness(cs.clone(), || Ok(U)).unwrap();
692
693        let v = IPAGadget::<Projective, GVar, hiding>::verify::<k>(
694            &gVar,
695            &hVar,
696            &challengeVar,
697            &vVar,
698            &cmVar,
699            &proofVar,
700            &r_blindVar,
701            &uVar,
702            &UVar,
703        )
704        .unwrap();
705        v.enforce_equal(&Boolean::TRUE).unwrap();
706        assert!(cs.is_satisfied().unwrap());
707    }
708}