1// code forked from:
  2// https://github.com/EspressoSystems/hyperplonk/tree/main/subroutines/src/poly_iop/sum_check
  3//
  4// Copyright (c) 2023 Espresso Systems (espressosys.com)
  5// This file is part of the HyperPlonk library.
  6
  7// You should have received a copy of the MIT License
  8// along with the HyperPlonk library. If not, see <https://mit-license.org/>.
  9
 10//! Verifier subroutines for a SumCheck protocol.
 11
 12use super::{
 13    structs::{IOPProverMessage, IOPVerifierState},
 14    SumCheckSubClaim, SumCheckVerifier,
 15};
 16use crate::{transcript::Transcript, utils::virtual_polynomial::VPAuxInfo};
 17use ark_ec::CurveGroup;
 18use ark_ff::PrimeField;
 19use ark_poly::Polynomial;
 20use ark_poly::{univariate::DensePolynomial, DenseUVPolynomial};
 21use ark_std::{end_timer, start_timer};
 22use espresso_subroutines::poly_iop::prelude::PolyIOPErrors;
 23
 24#[cfg(feature = "parallel")]
 25use rayon::iter::{IndexedParallelIterator, IntoParallelIterator, ParallelIterator};
 26
 27impl<C: CurveGroup> SumCheckVerifier<C> for IOPVerifierState<C> {
 28    type VPAuxInfo = VPAuxInfo<C::ScalarField>;
 29    type ProverMessage = IOPProverMessage<C::ScalarField>;
 30    type Challenge = C::ScalarField;
 31    type SumCheckSubClaim = SumCheckSubClaim<C::ScalarField>;
 32
 33    /// Initialize the verifier's state.
 34    fn verifier_init(index_info: &Self::VPAuxInfo) -> Self {
 35        let start = start_timer!(|| "sum check verifier init");
 36        let res = Self {
 37            round: 1,
 38            num_vars: index_info.num_variables,
 39            finished: false,
 40            polynomials_received: Vec::with_capacity(index_info.num_variables),
 41            challenges: Vec::with_capacity(index_info.num_variables),
 42        };
 43        end_timer!(start);
 44        res
 45    }
 46
 47    fn verify_round_and_update_state(
 48        &mut self,
 49        prover_msg: &<IOPVerifierState<C> as SumCheckVerifier<C>>::ProverMessage,
 50        transcript: &mut impl Transcript<C>,
 51    ) -> Result<<IOPVerifierState<C> as SumCheckVerifier<C>>::Challenge, PolyIOPErrors> {
 52        let start =
 53            start_timer!(|| format!("sum check verify {}-th round and update state", self.round));
 54
 55        if self.finished {
 56            return Err(PolyIOPErrors::InvalidVerifier(
 57                "Incorrect verifier state: Verifier is already finished.".to_string(),
 58            ));
 59        }
 60
 61        // In an interactive protocol, the verifier should
 62        //
 63        // 1. check if the received 'P(0) + P(1) = expected`.
 64        // 2. set `expected` to P(r)`
 65        //
 66        // When we turn the protocol to a non-interactive one, it is sufficient to defer
 67        // such checks to `check_and_generate_subclaim` after the last round.
 68        let challenge = transcript.get_challenge();
 69        self.challenges.push(challenge);
 70        self.polynomials_received.push(prover_msg.coeffs.to_vec());
 71
 72        if self.round == self.num_vars {
 73            // accept and close
 74            self.finished = true;
 75        } else {
 76            // proceed to the next round
 77            self.round += 1;
 78        }
 79
 80        end_timer!(start);
 81        Ok(challenge)
 82    }
 83
 84    fn check_and_generate_subclaim(
 85        &self,
 86        asserted_sum: &C::ScalarField,
 87    ) -> Result<Self::SumCheckSubClaim, PolyIOPErrors> {
 88        let start = start_timer!(|| "sum check check and generate subclaim");
 89        if !self.finished {
 90            return Err(PolyIOPErrors::InvalidVerifier(
 91                "Incorrect verifier state: Verifier has not finished.".to_string(),
 92            ));
 93        }
 94
 95        if self.polynomials_received.len() != self.num_vars {
 96            return Err(PolyIOPErrors::InvalidVerifier(
 97                "insufficient rounds".to_string(),
 98            ));
 99        }
100
101        // the deferred check during the interactive phase:
102        // 2. set `expected` to P(r)`
103        #[cfg(feature = "parallel")]
104        let mut expected_vec = self
105            .polynomials_received
106            .clone()
107            .into_par_iter()
108            .zip(self.challenges.clone().into_par_iter())
109            .map(|(coeffs, challenge)| {
110                // Removed check on number of evaluations here since verifier receives polynomial in coeffs form
111                let prover_poly = DensePolynomial::from_coefficients_slice(&coeffs);
112                Ok(prover_poly.evaluate(&challenge))
113            })
114            .collect::<Result<Vec<_>, PolyIOPErrors>>()?;
115
116        #[cfg(not(feature = "parallel"))]
117        let mut expected_vec = self
118            .polynomials_received
119            .clone()
120            .into_iter()
121            .zip(self.challenges.clone().into_iter())
122            .map(|(coeffs, challenge)| {
123                // Removed check on number of evaluations here since verifier receives polynomial in coeffs form
124                let prover_poly = DensePolynomial::from_coefficients_slice(&coeffs);
125                Ok(prover_poly.evaluate(&challenge))
126            })
127            .collect::<Result<Vec<_>, PolyIOPErrors>>()?;
128
129        // insert the asserted_sum to the first position of the expected vector
130        expected_vec.insert(0, *asserted_sum);
131
132        for (coeffs, &expected) in self
133            .polynomials_received
134            .iter()
135            .zip(expected_vec.iter())
136            .take(self.num_vars)
137        {
138            let poly = DensePolynomial::from_coefficients_slice(coeffs);
139            let eval_at_one: C::ScalarField = poly.iter().sum();
140            let eval_at_zero: C::ScalarField = poly.coeffs[0];
141            let eval = eval_at_one + eval_at_zero;
142
143            // the deferred check during the interactive phase:
144            // 1. check if the received 'P(0) + P(1) = expected`.
145            if eval != expected {
146                return Err(PolyIOPErrors::InvalidProof(
147                    "Prover message is not consistent with the claim.".to_string(),
148                ));
149            }
150        }
151        end_timer!(start);
152        Ok(SumCheckSubClaim {
153            point: self.challenges.clone(),
154            // the last expected value (not checked within this function) will be included in the
155            // subclaim
156            expected_evaluation: expected_vec[self.num_vars],
157        })
158    }
159}
160
161/// Interpolate a uni-variate degree-`p_i.len()-1` polynomial and evaluate this
162/// polynomial at `eval_at`:
163///
164///   \sum_{i=0}^len p_i * (\prod_{j!=i} (eval_at - j)/(i-j) )
165///
166/// This implementation is linear in number of inputs in terms of field
167/// operations. It also has a quadratic term in primitive operations which is
168/// negligible compared to field operations.
169/// TODO: The quadratic term can be removed by precomputing the lagrange
170/// coefficients.
171pub fn interpolate_uni_poly<F: PrimeField>(p_i: &[F], eval_at: F) -> Result<F, PolyIOPErrors> {
172    let start = start_timer!(|| "sum check interpolate uni poly opt");
173
174    let len = p_i.len();
175    let mut evals = vec![];
176    let mut prod = eval_at;
177    evals.push(eval_at);
178
179    // `prod = \prod_{j} (eval_at - j)`
180    for e in 1..len {
181        let tmp = eval_at - F::from(e as u64);
182        evals.push(tmp);
183        prod *= tmp;
184    }
185    let mut res = F::zero();
186    // we want to compute \prod (j!=i) (i-j) for a given i
187    //
188    // we start from the last step, which is
189    //  denom[len-1] = (len-1) * (len-2) *... * 2 * 1
190    // the step before that is
191    //  denom[len-2] = (len-2) * (len-3) * ... * 2 * 1 * -1
192    // and the step before that is
193    //  denom[len-3] = (len-3) * (len-4) * ... * 2 * 1 * -1 * -2
194    //
195    // i.e., for any i, the one before this will be derived from
196    //  denom[i-1] = denom[i] * (len-i) / i
197    //
198    // that is, we only need to store
199    // - the last denom for i = len-1, and
200    // - the ratio between current step and fhe last step, which is the product of
201    //   (len-i) / i from all previous steps and we store this product as a fraction
202    //   number to reduce field divisions.
203
204    // We know
205    //  - 2^61 < factorial(20) < 2^62
206    //  - 2^122 < factorial(33) < 2^123
207    // so we will be able to compute the ratio
208    //  - for len <= 20 with i64
209    //  - for len <= 33 with i128
210    //  - for len >  33 with BigInt
211    if p_i.len() <= 20 {
212        let last_denominator = F::from(u64_factorial(len - 1));
213        let mut ratio_numerator = 1i64;
214        let mut ratio_denominator = 1u64;
215
216        for i in (0..len).rev() {
217            let ratio_numerator_f = if ratio_numerator < 0 {
218                -F::from((-ratio_numerator) as u64)
219            } else {
220                F::from(ratio_numerator as u64)
221            };
222
223            res += p_i[i] * prod * F::from(ratio_denominator)
224                / (last_denominator * ratio_numerator_f * evals[i]);
225
226            // compute denom for the next step is current_denom * (len-i)/i
227            if i != 0 {
228                ratio_numerator *= -(len as i64 - i as i64);
229                ratio_denominator *= i as u64;
230            }
231        }
232    } else if p_i.len() <= 33 {
233        let last_denominator = F::from(u128_factorial(len - 1));
234        let mut ratio_numerator = 1i128;
235        let mut ratio_denominator = 1u128;
236
237        for i in (0..len).rev() {
238            let ratio_numerator_f = if ratio_numerator < 0 {
239                -F::from((-ratio_numerator) as u128)
240            } else {
241                F::from(ratio_numerator as u128)
242            };
243
244            res += p_i[i] * prod * F::from(ratio_denominator)
245                / (last_denominator * ratio_numerator_f * evals[i]);
246
247            // compute denom for the next step is current_denom * (len-i)/i
248            if i != 0 {
249                ratio_numerator *= -(len as i128 - i as i128);
250                ratio_denominator *= i as u128;
251            }
252        }
253    } else {
254        let mut denom_up = field_factorial::<F>(len - 1);
255        let mut denom_down = F::one();
256
257        for i in (0..len).rev() {
258            res += p_i[i] * prod * denom_down / (denom_up * evals[i]);
259
260            // compute denom for the next step is current_denom * (len-i)/i
261            if i != 0 {
262                denom_up *= -F::from((len - i) as u64);
263                denom_down *= F::from(i as u64);
264            }
265        }
266    }
267    end_timer!(start);
268    Ok(res)
269}
270
271/// compute the factorial(a) = 1 * 2 * ... * a
272#[inline]
273fn field_factorial<F: PrimeField>(a: usize) -> F {
274    let mut res = F::one();
275    for i in 2..=a {
276        res *= F::from(i as u64);
277    }
278    res
279}
280
281/// compute the factorial(a) = 1 * 2 * ... * a
282#[inline]
283fn u128_factorial(a: usize) -> u128 {
284    let mut res = 1u128;
285    for i in 2..=a {
286        res *= i as u128;
287    }
288    res
289}
290
291/// compute the factorial(a) = 1 * 2 * ... * a
292#[inline]
293fn u64_factorial(a: usize) -> u64 {
294    let mut res = 1u64;
295    for i in 2..=a {
296        res *= i as u64;
297    }
298    res
299}