testudo/README.md
README.mdRaw
1# Spartan: High-speed zkSNARKs without trusted setup
2
3
4[](<(https://crates.io/crates/spartan)>)
5
6Spartan 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](https://eprint.iacr.org/2019/550) published at [CRYPTO 2020](https://crypto.iacr.org/2020/). The security of the Spartan variant implemented in this library is based on the discrete logarithm problem in the random oracle model.
7
8A 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](https://eprint.iacr.org/2020/758.pdf) for an overview and this [paper](https://eprint.iacr.org/2018/907.pdf) for details.
9
10Note that this library has _not_ received a security review or audit.
11
12## Highlights
13
14We now highlight Spartan's distinctive features.
15
16- **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.
17
18- **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.
19
20- **Sub-linear verification costs:** Spartan is the first transparent proof system with sub-linear verification costs for arbitrary NP statements (e.g., R1CS).
21
22- **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`](https://docs.rs/curve25519-dalek) for arithmetic over `ristretto255`.
23
24- **State-of-the-art performance:**
25 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.
26
27### Implementation details
28
29`libspartan` uses [`merlin`](https://docs.rs/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.
30
31## Examples
32
33To import `libspartan` into your Rust project, add the following dependency to `Cargo.toml`:
34
35```text
36spartan = "0.4.1"
37```
38
39The following example shows how to use `libspartan` to create and verify a SNARK proof.
40Some of our public APIs' style is inspired by the underlying crates we use.
41
42```rust
43# extern crate libspartan;
44# extern crate merlin;
45# use libspartan::{Instance, SNARKGens, SNARK};
46# use merlin::Transcript;
47# fn main() {
48 // specify the size of an R1CS instance
49 let num_vars = 1024;
50 let num_cons = 1024;
51 let num_inputs = 10;
52 let num_non_zero_entries = 1024;
53
54 // produce public parameters
55 let gens = SNARKGens::new(num_cons, num_vars, num_inputs, num_non_zero_entries);
56
57 // ask the library to produce a synthentic R1CS instance
58 let (inst, vars, inputs) = Instance::produce_synthetic_r1cs(num_cons, num_vars, num_inputs);
59
60 // create a commitment to the R1CS instance
61 let (comm, decomm) = SNARK::encode(&inst, &gens);
62
63 // produce a proof of satisfiability
64 let mut prover_transcript = Transcript::new(b"snark_example");
65 let proof = SNARK::prove(&inst, &comm, &decomm, vars, &inputs, &gens, &mut prover_transcript);
66
67 // verify the proof of satisfiability
68 let mut verifier_transcript = Transcript::new(b"snark_example");
69 assert!(proof
70 .verify(&comm, &inputs, &mut verifier_transcript, &gens)
71 .is_ok());
72 println!("proof verification successful!");
73# }
74```
75
76Here is another example to use the NIZK variant of the Spartan proof system:
77
78```rust
79# extern crate libspartan;
80# extern crate merlin;
81# use libspartan::{Instance, NIZKGens, NIZK};
82# use merlin::Transcript;
83# fn main() {
84 // specify the size of an R1CS instance
85 let num_vars = 1024;
86 let num_cons = 1024;
87 let num_inputs = 10;
88
89 // produce public parameters
90 let gens = NIZKGens::new(num_cons, num_vars, num_inputs);
91
92 // ask the library to produce a synthentic R1CS instance
93 let (inst, vars, inputs) = Instance::produce_synthetic_r1cs(num_cons, num_vars, num_inputs);
94
95 // produce a proof of satisfiability
96 let mut prover_transcript = Transcript::new(b"nizk_example");
97 let proof = NIZK::prove(&inst, vars, &inputs, &gens, &mut prover_transcript);
98
99 // verify the proof of satisfiability
100 let mut verifier_transcript = Transcript::new(b"nizk_example");
101 assert!(proof
102 .verify(&inst, &inputs, &mut verifier_transcript, &gens)
103 .is_ok());
104 println!("proof verification successful!");
105# }
106```
107
108Finally, we provide an example that specifies a custom R1CS instance instead of using a synthetic instance
109
110```rust
111#![allow(non_snake_case)]
112# extern crate curve25519_dalek;
113# extern crate libspartan;
114# extern crate merlin;
115# use curve25519_dalek::scalar::Scalar;
116# use libspartan::{InputsAssignment, Instance, SNARKGens, VarsAssignment, SNARK};
117# use merlin::Transcript;
118# use rand::rngs::OsRng;
119# fn main() {
120 // produce a tiny instance
121 let (
122 num_cons,
123 num_vars,
124 num_inputs,
125 num_non_zero_entries,
126 inst,
127 assignment_vars,
128 assignment_inputs,
129 ) = produce_tiny_r1cs();
130
131 // produce public parameters
132 let gens = SNARKGens::new(num_cons, num_vars, num_inputs, num_non_zero_entries);
133
134 // create a commitment to the R1CS instance
135 let (comm, decomm) = SNARK::encode(&inst, &gens);
136
137 // produce a proof of satisfiability
138 let mut prover_transcript = Transcript::new(b"snark_example");
139 let proof = SNARK::prove(
140 &inst,
141 &comm,
142 &decomm,
143 assignment_vars,
144 &assignment_inputs,
145 &gens,
146 &mut prover_transcript,
147 );
148
149 // verify the proof of satisfiability
150 let mut verifier_transcript = Transcript::new(b"snark_example");
151 assert!(proof
152 .verify(&comm, &assignment_inputs, &mut verifier_transcript, &gens)
153 .is_ok());
154 println!("proof verification successful!");
155# }
156
157# fn produce_tiny_r1cs() -> (
158# usize,
159# usize,
160# usize,
161# usize,
162# Instance,
163# VarsAssignment,
164# InputsAssignment,
165# ) {
166 // We will use the following example, but one could construct any R1CS instance.
167 // Our R1CS instance is three constraints over five variables and two public inputs
168 // (Z0 + Z1) * I0 - Z2 = 0
169 // (Z0 + I1) * Z2 - Z3 = 0
170 // Z4 * 1 - 0 = 0
171
172 // parameters of the R1CS instance rounded to the nearest power of two
173 let num_cons = 4;
174 let num_vars = 5;
175 let num_inputs = 2;
176 let num_non_zero_entries = 5;
177
178 // We will encode the above constraints into three matrices, where
179 // the coefficients in the matrix are in the little-endian byte order
180 let mut A: Vec<(usize, usize, [u8; 32])> = Vec::new();
181 let mut B: Vec<(usize, usize, [u8; 32])> = Vec::new();
182 let mut C: Vec<(usize, usize, [u8; 32])> = Vec::new();
183
184 // The constraint system is defined over a finite field, which in our case is
185 // the scalar field of ristreeto255/curve25519 i.e., p = 2^{252}+27742317777372353535851937790883648493
186 // To construct these matrices, we will use `curve25519-dalek` but one can use any other method.
187
188 // a variable that holds a byte representation of 1
189 let one = Scalar::one().to_bytes();
190
191 // R1CS is a set of three sparse matrices A B C, where is a row for every
192 // constraint and a column for every entry in z = (vars, 1, inputs)
193 // An R1CS instance is satisfiable iff:
194 // Az \circ Bz = Cz, where z = (vars, 1, inputs)
195
196 // constraint 0 entries in (A,B,C)
197 // constraint 0 is (Z0 + Z1) * I0 - Z2 = 0.
198 // We set 1 in matrix A for columns that correspond to Z0 and Z1
199 // We set 1 in matrix B for column that corresponds to I0
200 // We set 1 in matrix C for column that corresponds to Z2
201 A.push((0, 0, one));
202 A.push((0, 1, one));
203 B.push((0, num_vars + 1, one));
204 C.push((0, 2, one));
205
206 // constraint 1 entries in (A,B,C)
207 A.push((1, 0, one));
208 A.push((1, num_vars + 2, one));
209 B.push((1, 2, one));
210 C.push((1, 3, one));
211
212 // constraint 3 entries in (A,B,C)
213 A.push((2, 4, one));
214 B.push((2, num_vars, one));
215
216 let inst = Instance::new(num_cons, num_vars, num_inputs, &A, &B, &C).unwrap();
217
218 // compute a satisfying assignment
219let mut rng = ark_std::rand::thread_rng();
220 let i0 = Scalar::rand(&mut rng);
221 let i1 = Scalar::rand(&mut rng);
222 let z0 = Scalar::rand(&mut rng);
223 let z1 = Scalar::rand(&mut rng);
224 let z2 = (z0 + z1) * i0; // constraint 0
225 let z3 = (z0 + i1) * z2; // constraint 1
226 let z4 = Scalar::zero(); //constraint 2
227
228 // create a VarsAssignment
229 let mut vars = vec![Scalar::zero().to_bytes(); num_vars];
230 vars[0] = z0.to_bytes();
231 vars[1] = z1.to_bytes();
232 vars[2] = z2.to_bytes();
233 vars[3] = z3.to_bytes();
234 vars[4] = z4.to_bytes();
235 let assignment_vars = VarsAssignment::new(&vars).unwrap();
236
237 // create an InputsAssignment
238 let mut inputs = vec![Scalar::zero().to_bytes(); num_inputs];
239 inputs[0] = i0.to_bytes();
240 inputs[1] = i1.to_bytes();
241 let assignment_inputs = InputsAssignment::new(&inputs).unwrap();
242
243 // check if the instance we created is satisfiable
244 let res = inst.is_sat(&assignment_vars, &assignment_inputs);
245 assert_eq!(res.unwrap(), true);
246
247 (
248 num_cons,
249 num_vars,
250 num_inputs,
251 num_non_zero_entries,
252 inst,
253 assignment_vars,
254 assignment_inputs,
255 )
256# }
257```
258
259For more examples, see [`examples/`](examples) directory in this repo.
260
261## Building `libspartan`
262
263Install [`rustup`](https://rustup.rs/)
264
265Switch to nightly Rust using `rustup`:
266
267```text
268rustup default nightly
269```
270
271Clone the repository:
272
273```text
274git clone https://github.com/Microsoft/Spartan
275cd Spartan
276```
277
278To build docs for public APIs of `libspartan`:
279
280```text
281cargo doc
282```
283
284To run tests:
285
286```text
287RUSTFLAGS="-C target_cpu=native" cargo test
288```
289
290To build `libspartan`:
291
292```text
293RUSTFLAGS="-C target_cpu=native" cargo build --release
294```
295
296> 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`.
297
298### Supported features
299
300- `profile`: enables fine-grained profiling information (see below for its use)
301
302## Performance
303
304### End-to-end benchmarks
305
306`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).
307
308To run end-to-end benchmarks:
309
310```text
311RUSTFLAGS="-C target_cpu=native" cargo bench
312```
313
314### Fine-grained profiling
315
316Build `libspartan` with `profile` feature enabled. It creates two profilers: `./target/release/snark` and `./target/release/nizk`.
317
318These profilers report performance as depicted below (for varying R1CS instance sizes). The reported
319performance 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).
320See Section 9 in our [paper](https://eprint.iacr.org/2019/550) to see how this compares with other zkSNARKs in the literature.
321
322```text
323$ ./target/release/snark
324Profiler:: SNARK
325 * number_of_constraints 1048576
326 * number_of_variables 1048576
327 * number_of_inputs 10
328 * number_non-zero_entries_A 1048576
329 * number_non-zero_entries_B 1048576
330 * number_non-zero_entries_C 1048576
331 * SNARK::encode
332 * SNARK::encode 14.2644201s
333 * SNARK::prove
334 * R1CSProof::prove
335 * polycommit
336 * polycommit 2.7175848s
337 * prove_sc_phase_one
338 * prove_sc_phase_one 683.7481ms
339 * prove_sc_phase_two
340 * prove_sc_phase_two 846.1056ms
341 * polyeval
342 * polyeval 193.4216ms
343 * R1CSProof::prove 4.4416193s
344 * len_r1cs_sat_proof 47024
345 * eval_sparse_polys
346 * eval_sparse_polys 377.357ms
347 * R1CSEvalProof::prove
348 * commit_nondet_witness
349 * commit_nondet_witness 14.4507331s
350 * build_layered_network
351 * build_layered_network 3.4360521s
352 * evalproof_layered_network
353 * len_product_layer_proof 64712
354 * evalproof_layered_network 15.5708066s
355 * R1CSEvalProof::prove 34.2930559s
356 * len_r1cs_eval_proof 133720
357 * SNARK::prove 39.1297568s
358 * SNARK::proof_compressed_len 141768
359 * SNARK::verify
360 * verify_sat_proof
361 * verify_sat_proof 20.0828ms
362 * verify_eval_proof
363 * verify_polyeval_proof
364 * verify_prod_proof
365 * verify_prod_proof 1.1847ms
366 * verify_hash_proof
367 * verify_hash_proof 81.06ms
368 * verify_polyeval_proof 82.3583ms
369 * verify_eval_proof 82.8937ms
370 * SNARK::verify 103.0536ms
371```
372
373```text
374$ ./target/release/nizk
375Profiler:: NIZK
376 * number_of_constraints 1048576
377 * number_of_variables 1048576
378 * number_of_inputs 10
379 * number_non-zero_entries_A 1048576
380 * number_non-zero_entries_B 1048576
381 * number_non-zero_entries_C 1048576
382 * NIZK::prove
383 * R1CSProof::prove
384 * polycommit
385 * polycommit 2.7220635s
386 * prove_sc_phase_one
387 * prove_sc_phase_one 722.5487ms
388 * prove_sc_phase_two
389 * prove_sc_phase_two 862.6796ms
390 * polyeval
391 * polyeval 190.2233ms
392 * R1CSProof::prove 4.4982305s
393 * len_r1cs_sat_proof 47024
394 * NIZK::prove 4.5139888s
395 * NIZK::proof_compressed_len 48134
396 * NIZK::verify
397 * eval_sparse_polys
398 * eval_sparse_polys 395.0847ms
399 * verify_sat_proof
400 * verify_sat_proof 19.286ms
401 * NIZK::verify 414.5102ms
402```
403
404## LICENSE
405
406See [LICENSE](./LICENSE)
407
408## Contributing
409
410See [CONTRIBUTING](./CONTRIBUTING.md)