Spartan: High-speed zkSNARKs without trusted setup

Spartan is a high-speed zero-knowledge proof system, a cryptographic primitive that enables a prover to prove a mathematical statement to a verifier without revealing anything besides the validity of the statement. This repository provides libspartan, a Rust library that implements a zero-knowledge succinct non-interactive argument of knowledge (zkSNARK), which is a type of zero-knowledge proof system with short proofs and fast verification times. The details of the Spartan proof system are described in our paper published at CRYPTO 2020. The security of the Spartan variant implemented in this library is based on the discrete logarithm problem in the random oracle model.

A simple example application is proving the knowledge of a secret s such that H(s) == d for a public d, where H is a cryptographic hash function (e.g., SHA-256, Keccak). A more complex application is a database-backed cloud service that produces proofs of correct state machine transitions for auditability. See this paper for an overview and this paper for details.

Note that this library has not received a security review or audit.

Highlights

We now highlight Spartan's distinctive features.

• No "toxic" waste: Spartan is a transparent zkSNARK and does not require a trusted setup. So, it does not involve any trapdoors that must be kept secret or require a multi-party ceremony to produce public parameters.

• General-purpose: Spartan produces proofs for arbitrary NP statements. libspartan supports NP statements expressed as rank-1 constraint satisfiability (R1CS) instances, a popular language for which there exists efficient transformations and compiler toolchains from high-level programs of interest.

• Sub-linear verification costs and linear-time proving costs: Spartan is the first transparent proof system with sub-linear verification costs for arbitrary NP statements (e.g., R1CS). Spartan also features a linear-time prover, a property that has remained elusive for nearly all zkSNARKs in the literature.

• Standardized security: Spartan's security relies on the hardness of computing discrete logarithms (a standard cryptographic assumption) in the random oracle model. libspartan uses ristretto255, a prime-order group abstraction atop curve25519 (a high-speed elliptic curve). We use curve25519-dalek for arithmetic over ristretto255.

• State-of-the-art performance: Among transparent SNARKs, Spartan offers the fastest prover with speedups of 36–152× depending on the baseline, produces proofs that are shorter by 1.2–416×, and incurs the lowest verification times with speedups of 3.6–1326×. The only exception is proof sizes under Bulletproofs, but Bulletproofs incurs slower verification both asymptotically and concretely. When compared to the state-of-the-art zkSNARK with trusted setup, Spartan’s prover is 2× faster for arbitrary R1CS instances and 16× faster for data-parallel workloads.

Implementation details

libspartan uses merlin to automate the Fiat-Shamir transform. We also introduce a new type called RandomTape that extends a Transcript in merlin to allow the prover's internal methods to produce private randomness using its private transcript without having to create OsRng objects throughout the code. An object of type RandomTape is initialized with a new random seed from OsRng for each proof produced by the library.

Examples

To import libspartan into your Rust project, add the following dependency to Cargo.toml:

spartan = "0.2.1"

The following example shows how to use libspartan to create and verify a SNARK proof. Some of our public APIs' style is inspired by the underlying crates we use.

# extern crate libspartan;
# extern crate merlin;
# use libspartan::{Instance, SNARKGens, SNARK};
# use merlin::Transcript;
# fn main() {
    // specify the size of an R1CS instance
    let num_vars = 1024;
    let num_cons = 1024;
    let num_inputs = 10;
    let num_non_zero_entries = 1024;

    // produce public parameters
    let gens = SNARKGens::new(num_cons, num_vars, num_inputs, num_non_zero_entries);

    // ask the library to produce a synthentic R1CS instance
    let (inst, vars, inputs) = Instance::produce_synthetic_r1cs(num_cons, num_vars, num_inputs);

    // create a commitment to the R1CS instance
    let (comm, decomm) = SNARK::encode(&inst, &gens);

    // produce a proof of satisfiability
    let mut prover_transcript = Transcript::new(b"snark_example");
    let proof = SNARK::prove(&inst, &decomm, vars, &inputs, &gens, &mut prover_transcript);

    // verify the proof of satisfiability
    let mut verifier_transcript = Transcript::new(b"snark_example");
    assert!(proof
      .verify(&comm, &inputs, &mut verifier_transcript, &gens)
      .is_ok());
    println!("proof verification successful!");
# }

Here is another example to use the NIZK variant of the Spartan proof system:

# extern crate libspartan;
# extern crate merlin;
# use libspartan::{Instance, NIZKGens, NIZK};
# use merlin::Transcript;
# fn main() {
    // specify the size of an R1CS instance
    let num_vars = 1024;
    let num_cons = 1024;
    let num_inputs = 10;

    // produce public parameters
    let gens = NIZKGens::new(num_cons, num_vars);

    // ask the library to produce a synthentic R1CS instance
    let (inst, vars, inputs) = Instance::produce_synthetic_r1cs(num_cons, num_vars, num_inputs);

    // produce a proof of satisfiability
    let mut prover_transcript = Transcript::new(b"nizk_example");
    let proof = NIZK::prove(&inst, vars, &inputs, &gens, &mut prover_transcript);

    // verify the proof of satisfiability
    let mut verifier_transcript = Transcript::new(b"nizk_example");
    assert!(proof
      .verify(&inst, &inputs, &mut verifier_transcript, &gens)
      .is_ok());
    println!("proof verification successful!");
# }

Finally, we provide an example that specifies a custom R1CS instance instead of using a synthetic instance

# extern crate curve25519_dalek;
# extern crate libspartan;
# extern crate merlin;
# use curve25519_dalek::scalar::Scalar;
# use libspartan::{InputsAssignment, Instance, SNARKGens, VarsAssignment, SNARK};
# use merlin::Transcript;
# use rand::rngs::OsRng;
# fn main() {
  // produce a tiny instance
  let (
    num_cons,
    num_vars,
    num_inputs,
    num_non_zero_entries,
    inst,
    assignment_vars,
    assignment_inputs,
  ) = produce_tiny_r1cs();

  // produce public parameters
  let gens = SNARKGens::new(num_cons, num_vars, num_inputs, num_non_zero_entries);

  // create a commitment to the R1CS instance
  let (comm, decomm) = SNARK::encode(&inst, &gens);

  // produce a proof of satisfiability
  let mut prover_transcript = Transcript::new(b"snark_example");
  let proof = SNARK::prove(
    &inst,
    &decomm,
    assignment_vars,
    &assignment_inputs,
    &gens,
    &mut prover_transcript,
  );

  // verify the proof of satisfiability
  let mut verifier_transcript = Transcript::new(b"snark_example");
  assert!(proof
    .verify(&comm, &assignment_inputs, &mut verifier_transcript, &gens)
    .is_ok());
  println!("proof verification successful!");
# }

# fn produce_tiny_r1cs() -> (
#  usize,
#  usize,
#  usize,
#  usize,
#  Instance,
#  VarsAssignment,
#  InputsAssignment,
# ) {
  // We will use the following example, but one could construct any R1CS instance.
  // Our R1CS instance is three constraints over five variables and two public inputs
  // (Z0 + Z1) * I0 - Z2 = 0
  // (Z0 + I1) * Z2 - Z3 = 0
  // Z4 * 1 - 0 = 0

  // parameters of the R1CS instance rounded to the nearest power of two
  let num_cons = 4;
  let num_vars = 8;
  let num_inputs = 2;
  let num_non_zero_entries = 8;

  // We will encode the above constraints into three matrices, where
  // the coefficients in the matrix are in the little-endian byte order
  let mut A: Vec<(usize, usize, [u8; 32])> = Vec::new();
  let mut B: Vec<(usize, usize, [u8; 32])> = Vec::new();
  let mut C: Vec<(usize, usize, [u8; 32])> = Vec::new();

  // The constraint system is defined over a finite field, which in our case is
  // the scalar field of ristreeto255/curve25519 i.e., p =  2^{252}+27742317777372353535851937790883648493
  // To construct these matrices, we will use `curve25519-dalek` but one can use any other method.

  // a variable that holds a byte representation of 1
  let one = Scalar::one().to_bytes();

  // R1CS is a set of three sparse matrices A B C, where is a row for every 
  // constraint and a column for every entry in z = (vars, 1, inputs)
  // An R1CS instance is satisfiable iff:
  // Az \circ Bz = Cz, where z = (vars, 1, inputs)

  // constraint 0 entries in (A,B,C)
  // constraint 0 is (Z0 + Z1) * I0 - Z2 = 0.
  // We set 1 in matrix A for columns that correspond to Z0 and Z1
  // We set 1 in matrix B for column that corresponds to I0
  // We set 1 in matrix C for column that corresponds to Z2
  A.push((0, 0, one));
  A.push((0, 1, one));
  B.push((0, num_vars + 1, one));
  C.push((0, 2, one));

  // constraint 1 entries in (A,B,C)
  A.push((1, 0, one));
  A.push((1, num_vars + 2, one));
  B.push((1, 2, one));
  C.push((1, 3, one));

  // constraint 3 entries in (A,B,C)
  A.push((2, 4, one));
  B.push((2, num_vars, one));

  let inst = Instance::new(num_cons, num_vars, num_inputs, &A, &B, &C).unwrap();

  // compute a satisfying assignment
  let mut csprng: OsRng = OsRng;
  let i0 = Scalar::random(&mut csprng);
  let i1 = Scalar::random(&mut csprng);
  let z0 = Scalar::random(&mut csprng);
  let z1 = Scalar::random(&mut csprng);
  let z2 = (z0 + z1) * i0; // constraint 0
  let z3 = (z0 + i1) * z2; // constraint 1
  let z4 = Scalar::zero(); //constraint 2

  // create a VarsAssignment
  let mut vars = vec![Scalar::zero().to_bytes(); num_vars];
  vars[0] = z0.to_bytes();
  vars[1] = z1.to_bytes();
  vars[2] = z2.to_bytes();
  vars[3] = z3.to_bytes();
  vars[4] = z4.to_bytes();
  let assignment_vars = VarsAssignment::new(&vars).unwrap();

  // create an InputsAssignment
  let mut inputs = vec![Scalar::zero().to_bytes(); num_inputs];
  inputs[0] = i0.to_bytes();
  inputs[1] = i1.to_bytes();
  let assignment_inputs = InputsAssignment::new(&inputs).unwrap();
  
  // check if the instance we created is satisfiable
  let res = inst.is_sat(&assignment_vars, &assignment_inputs);
  assert_eq!(res.unwrap(), true);

  (
    num_cons,
    num_vars,
    num_inputs,
    num_non_zero_entries,
    inst,
    assignment_vars,
    assignment_inputs,
  )
# }

For more examples, see examples/ directory in this repo.

Building libspartan

Install rustup

Switch to nightly Rust using rustup:

rustup default nightly

Clone the repository:

git clone https://github.com/Microsoft/Spartan
cd Spartan

To build docs for public APIs of libspartan:

cargo doc

To run tests:

RUSTFLAGS="-C target_cpu=native" cargo test

To build libspartan:

RUSTFLAGS="-C target_cpu=native" cargo build --release

NOTE: We enable SIMD instructions in curve25519-dalek by default, so if it fails to build remove the "simd_backend" feature argument in Cargo.toml.

Supported features

• profile: enables fine-grained profiling information (see below for its use)

Performance

End-to-end benchmarks

libspartan includes two benches: benches/nizk.rs and benches/snark.rs. If you report the performance of Spartan in a research paper, we recommend using these benches for higher accuracy instead of fine-grained profiling (listed below).

To run end-to-end benchmarks:

RUSTFLAGS="-C target_cpu=native" cargo bench

Fine-grained profiling

Build libspartan with profile feature enabled. It creates two profilers: ./target/release/snark and ./target/release/nizk.

These profilers report performance as depicted below (for varying R1CS instance sizes). The reported performance is from running the profilers on a Microsoft Surface Laptop 3 on a single CPU core of Intel Core i7-1065G7 running Ubuntu 20.04 (atop WSL2 on Windows 10). See Section 9 in our paper to see how this compares with other zkSNARKs in the literature.

$ ./target/release/snark 
Profiler:: SNARK
  * number_of_constraints 1048576
  * number_of_variables 1048576
  * number_of_inputs 10
  * number_non-zero_entries_A 1048576
  * number_non-zero_entries_B 1048576
  * number_non-zero_entries_C 1048576
  * SNARK::encode
  * SNARK::encode 14.2644201s
  * SNARK::prove
    * R1CSProof::prove
      * polycommit
      * polycommit 2.7175848s
      * prove_sc_phase_one
      * prove_sc_phase_one 683.7481ms
      * prove_sc_phase_two
      * prove_sc_phase_two 846.1056ms
      * polyeval
      * polyeval 193.4216ms
    * R1CSProof::prove 4.4416193s
    * len_r1cs_sat_proof 47024
    * eval_sparse_polys
    * eval_sparse_polys 377.357ms
    * R1CSEvalProof::prove
      * commit_nondet_witness
      * commit_nondet_witness 14.4507331s
      * build_layered_network
      * build_layered_network 3.4360521s
      * evalproof_layered_network
        * len_product_layer_proof 64712
      * evalproof_layered_network 15.5708066s
    * R1CSEvalProof::prove 34.2930559s
    * len_r1cs_eval_proof 133720
  * SNARK::prove 39.1297568s
  * SNARK::proof_compressed_len 141768
  * SNARK::verify
    * verify_sat_proof
    * verify_sat_proof 20.0828ms
    * verify_eval_proof
      * verify_polyeval_proof
        * verify_prod_proof
        * verify_prod_proof 1.1847ms
        * verify_hash_proof
        * verify_hash_proof 81.06ms
      * verify_polyeval_proof 82.3583ms
    * verify_eval_proof 82.8937ms
  * SNARK::verify 103.0536ms

$ ./target/release/nizk 
Profiler:: NIZK
  * number_of_constraints 1048576
  * number_of_variables 1048576
  * number_of_inputs 10
  * number_non-zero_entries_A 1048576
  * number_non-zero_entries_B 1048576
  * number_non-zero_entries_C 1048576
  * NIZK::prove
    * R1CSProof::prove
      * polycommit
      * polycommit 2.7220635s
      * prove_sc_phase_one
      * prove_sc_phase_one 722.5487ms
      * prove_sc_phase_two
      * prove_sc_phase_two 862.6796ms
      * polyeval
      * polyeval 190.2233ms
    * R1CSProof::prove 4.4982305s
    * len_r1cs_sat_proof 47024
  * NIZK::prove 4.5139888s
  * NIZK::proof_compressed_len 48134
  * NIZK::verify
    * eval_sparse_polys
    * eval_sparse_polys 395.0847ms
    * verify_sat_proof
    * verify_sat_proof 19.286ms
  * NIZK::verify 414.5102ms

LICENSE

See LICENSE

Contributing

See CONTRIBUTING