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::{
 15  parameters::poseidon_params, poseidon_transcript::PoseidonTranscript, InputsAssignment, Instance,
 16  SNARKGens, VarsAssignment, SNARK,
 17};
 18
 19#[allow(non_snake_case)]
 20fn produce_r1cs() -> (
 21  usize,
 22  usize,
 23  usize,
 24  usize,
 25  Instance,
 26  VarsAssignment,
 27  InputsAssignment,
 28) {
 29  // parameters of the R1CS instance
 30  let num_cons = 4;
 31  let num_vars = 4;
 32  let num_inputs = 1;
 33  let num_non_zero_entries = 8;
 34
 35  // We will encode the above constraints into three matrices, where
 36  // the coefficients in the matrix are in the little-endian byte order
 37  let mut A: Vec<(usize, usize, Vec<u8>)> = Vec::new();
 38  let mut B: Vec<(usize, usize, Vec<u8>)> = Vec::new();
 39  let mut C: Vec<(usize, usize, Vec<u8>)> = Vec::new();
 40
 41  let one = Scalar::one().into_repr().to_bytes_le();
 42
 43  // R1CS is a set of three sparse matrices A B C, where is a row for every
 44  // constraint and a column for every entry in z = (vars, 1, inputs)
 45  // An R1CS instance is satisfiable iff:
 46  // Az \circ Bz = Cz, where z = (vars, 1, inputs)
 47
 48  // constraint 0 entries in (A,B,C)
 49  // constraint 0 is Z0 * Z0 - Z1 = 0.
 50  A.push((0, 0, one.clone()));
 51  B.push((0, 0, one.clone()));
 52  C.push((0, 1, one.clone()));
 53
 54  // constraint 1 entries in (A,B,C)
 55  // constraint 1 is Z1 * Z0 - Z2 = 0.
 56  A.push((1, 1, one.clone()));
 57  B.push((1, 0, one.clone()));
 58  C.push((1, 2, one.clone()));
 59
 60  // constraint 2 entries in (A,B,C)
 61  // constraint 2 is (Z2 + Z0) * 1 - Z3 = 0.
 62  A.push((2, 2, one.clone()));
 63  A.push((2, 0, one.clone()));
 64  B.push((2, num_vars, one.clone()));
 65  C.push((2, 3, one.clone()));
 66
 67  // constraint 3 entries in (A,B,C)
 68  // constraint 3 is (Z3 + 5) * 1 - I0 = 0.
 69  A.push((3, 3, one.clone()));
 70  A.push((3, num_vars, Scalar::from(5u32).into_repr().to_bytes_le()));
 71  B.push((3, num_vars, one.clone()));
 72  C.push((3, num_vars + 1, one.clone()));
 73
 74  let inst = Instance::new(num_cons, num_vars, num_inputs, &A, &B, &C).unwrap();
 75
 76  // compute a satisfying assignment
 77  let mut rng = ark_std::rand::thread_rng();
 78  let z0 = Scalar::rand(&mut rng);
 79  let z1 = z0 * z0; // constraint 0
 80  let z2 = z1 * z0; // constraint 1
 81  let z3 = z2 + z0; // constraint 2
 82  let i0 = z3 + Scalar::from(5u32); // constraint 3
 83
 84  // create a VarsAssignment
 85  let mut vars = vec![Scalar::zero().into_repr().to_bytes_le(); num_vars];
 86  vars[0] = z0.into_repr().to_bytes_le();
 87  vars[1] = z1.into_repr().to_bytes_le();
 88  vars[2] = z2.into_repr().to_bytes_le();
 89  vars[3] = z3.into_repr().to_bytes_le();
 90  let assignment_vars = VarsAssignment::new(&vars).unwrap();
 91
 92  // create an InputsAssignment
 93  let mut inputs = vec![Scalar::zero().into_repr().to_bytes_le(); num_inputs];
 94  inputs[0] = i0.into_repr().to_bytes_le();
 95  let assignment_inputs = InputsAssignment::new(&inputs).unwrap();
 96
 97  // check if the instance we created is satisfiable
 98  let res = inst.is_sat(&assignment_vars, &assignment_inputs);
 99  assert!(res.unwrap(), "should be satisfied");
100
101  (
102    num_cons,
103    num_vars,
104    num_inputs,
105    num_non_zero_entries,
106    inst,
107    assignment_vars,
108    assignment_inputs,
109  )
110}
111
112fn main() {
113  // produce an R1CS instance
114  let (
115    num_cons,
116    num_vars,
117    num_inputs,
118    num_non_zero_entries,
119    inst,
120    assignment_vars,
121    assignment_inputs,
122  ) = produce_r1cs();
123
124  let params = poseidon_params();
125
126  // produce public parameters
127  let gens = SNARKGens::new(num_cons, num_vars, num_inputs, num_non_zero_entries);
128
129  // create a commitment to the R1CS instance
130  let (comm, decomm) = SNARK::encode(&inst, &gens);
131
132  // produce a proof of satisfiability
133  let mut prover_transcript = PoseidonTranscript::new(&params);
134  let proof = SNARK::prove(
135    &inst,
136    &comm,
137    &decomm,
138    assignment_vars,
139    &assignment_inputs,
140    &gens,
141    &mut prover_transcript,
142  );
143
144  // verify the proof of satisfiability
145  let mut verifier_transcript = PoseidonTranscript::new(&params);
146  assert!(proof
147    .verify(&comm, &assignment_inputs, &mut verifier_transcript, &gens)
148    .is_ok());
149  println!("proof verification successful!");
150}