1//! Demonstrates how to produces a proof for canonical cubic equation: `x^3 + x + 5 = y`.
  2//! The example is described in detail [here].
  3//!
  4//! The R1CS for this problem consists of the following 4 constraints:
  5//! `Z0 * Z0 - Z1 = 0`
  6//! `Z1 * Z0 - Z2 = 0`
  7//! `(Z2 + Z0) * 1 - Z3 = 0`
  8//! `(Z3 + 5) * 1 - I0 = 0`
  9//!
 10//! [here]: https://medium.com/@VitalikButerin/quadratic-arithmetic-programs-from-zero-to-hero-f6d558cea649
 11use ark_bls12_377::Fr as Scalar;
 12use ark_ff::{BigInteger, PrimeField};
 13use ark_std::{One, UniformRand, Zero};
 14use libspartan::{InputsAssignment, Instance, SNARKGens, VarsAssignment, SNARK};
 15use merlin::Transcript;
 16
 17#[allow(non_snake_case)]
 18fn produce_r1cs() -> (
 19  usize,
 20  usize,
 21  usize,
 22  usize,
 23  Instance,
 24  VarsAssignment,
 25  InputsAssignment,
 26) {
 27  // parameters of the R1CS instance
 28  let num_cons = 4;
 29  let num_vars = 4;
 30  let num_inputs = 1;
 31  let num_non_zero_entries = 8;
 32
 33  // We will encode the above constraints into three matrices, where
 34  // the coefficients in the matrix are in the little-endian byte order
 35  let mut A: Vec<(usize, usize, Vec<u8>)> = Vec::new();
 36  let mut B: Vec<(usize, usize, Vec<u8>)> = Vec::new();
 37  let mut C: Vec<(usize, usize, Vec<u8>)> = Vec::new();
 38
 39  let one = Scalar::one().into_repr().to_bytes_le();
 40
 41  // R1CS is a set of three sparse matrices A B C, where is a row for every
 42  // constraint and a column for every entry in z = (vars, 1, inputs)
 43  // An R1CS instance is satisfiable iff:
 44  // Az \circ Bz = Cz, where z = (vars, 1, inputs)
 45
 46  // constraint 0 entries in (A,B,C)
 47  // constraint 0 is Z0 * Z0 - Z1 = 0.
 48  A.push((0, 0, one.clone()));
 49  B.push((0, 0, one.clone()));
 50  C.push((0, 1, one.clone()));
 51
 52  // constraint 1 entries in (A,B,C)
 53  // constraint 1 is Z1 * Z0 - Z2 = 0.
 54  A.push((1, 1, one.clone()));
 55  B.push((1, 0, one.clone()));
 56  C.push((1, 2, one.clone()));
 57
 58  // constraint 2 entries in (A,B,C)
 59  // constraint 2 is (Z2 + Z0) * 1 - Z3 = 0.
 60  A.push((2, 2, one.clone()));
 61  A.push((2, 0, one.clone()));
 62  B.push((2, num_vars, one.clone()));
 63  C.push((2, 3, one.clone()));
 64
 65  // constraint 3 entries in (A,B,C)
 66  // constraint 3 is (Z3 + 5) * 1 - I0 = 0.
 67  A.push((3, 3, one.clone()));
 68  A.push((3, num_vars, Scalar::from(5u32).into_repr().to_bytes_le()));
 69  B.push((3, num_vars, one.clone()));
 70  C.push((3, num_vars + 1, one.clone()));
 71
 72  let inst = Instance::new(num_cons, num_vars, num_inputs, &A, &B, &C).unwrap();
 73
 74  // compute a satisfying assignment
 75  let mut rng = ark_std::rand::thread_rng();
 76  let z0 = Scalar::rand(&mut rng);
 77  let z1 = z0 * z0; // constraint 0
 78  let z2 = z1 * z0; // constraint 1
 79  let z3 = z2 + z0; // constraint 2
 80  let i0 = z3 + Scalar::from(5u32); // constraint 3
 81
 82  // create a VarsAssignment
 83  let mut vars = vec![Scalar::zero().into_repr().to_bytes_le(); num_vars];
 84  vars[0] = z0.into_repr().to_bytes_le();
 85  vars[1] = z1.into_repr().to_bytes_le();
 86  vars[2] = z2.into_repr().to_bytes_le();
 87  vars[3] = z3.into_repr().to_bytes_le();
 88  let assignment_vars = VarsAssignment::new(&vars).unwrap();
 89
 90  // create an InputsAssignment
 91  let mut inputs = vec![Scalar::zero().into_repr().to_bytes_le(); num_inputs];
 92  inputs[0] = i0.into_repr().to_bytes_le();
 93  let assignment_inputs = InputsAssignment::new(&inputs).unwrap();
 94
 95  // check if the instance we created is satisfiable
 96  let res = inst.is_sat(&assignment_vars, &assignment_inputs);
 97  assert!(res.unwrap(), "should be satisfied");
 98
 99  (
100    num_cons,
101    num_vars,
102    num_inputs,
103    num_non_zero_entries,
104    inst,
105    assignment_vars,
106    assignment_inputs,
107  )
108}
109
110fn main() {
111  // produce an R1CS instance
112  let (
113    num_cons,
114    num_vars,
115    num_inputs,
116    num_non_zero_entries,
117    inst,
118    assignment_vars,
119    assignment_inputs,
120  ) = produce_r1cs();
121
122  // produce public parameters
123  let gens = SNARKGens::new(num_cons, num_vars, num_inputs, num_non_zero_entries);
124
125  // create a commitment to the R1CS instance
126  let (comm, decomm) = SNARK::encode(&inst, &gens);
127
128  // produce a proof of satisfiability
129  let mut prover_transcript = Transcript::new(b"snark_example");
130  let proof = SNARK::prove(
131    &inst,
132    &comm,
133    &decomm,
134    assignment_vars,
135    &assignment_inputs,
136    &gens,
137    &mut prover_transcript,
138  );
139
140  // verify the proof of satisfiability
141  let mut verifier_transcript = Transcript::new(b"snark_example");
142  assert!(proof
143    .verify(&comm, &assignment_inputs, &mut verifier_transcript, &gens)
144    .is_ok());
145  println!("proof verification successful!");
146}