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