test(VDF): add bench tests for VDF in rsa group

Cargo.toml

@@ -29,3 +29,8 @@ sha2 = "0.9.1"
 name = "bench-vdf-class"
 path = "benches/vdf/class_group.rs"
 harness = false
+
+[[bench]]
+name = "bench-vdf-rsa"
+path = "benches/vdf/rsa_group.rs"
+harness = false

README.md

@@ -41,14 +41,32 @@ Use `Cargo build`.
 The library uses bindings to PARI c library. Running `Cargo build` for the first time will take PARI from the _depend_ folder and install it on the machine. It was tested on MacOS and Linux. If you encounter a problem with installation of PARI, please open an issue and try to install it [manually](https://pari.math.u-bordeaux.fr/download.html). Bindings are generated automatically on the fly which might slow down the build procces by a few seconds.
 
 
-Test
+Unit-test
 -------------------
 Tests in rust are multi-thearded if possible. However, PARI configuration supports a single thread. Therefore to make sure all tests run with defined behaviour please use `cargo test  -- --test-threads=1`. 
 
 **Usage**
 
 We use tests to demonstrate correctness of each primitive: At the end of each primitive `.rs` file there is a test to show the correct usage of the primitive. There is usually one test or more to show soundness of the implementation, i.e. not knowing a witness will fail a PoK. For all tests we assume 128bit security (conservatively translates into 1600bit Discriminant).
 
+Bench-test
+-------------------
+Currenly this library supports benchmarking Wesolowski VDF in class_group vs in rsa_group. As aforementioned, PARI configuration only supports a single thread. To benchtest using PARI we need to use `--jobs 1` flag.
+
+You can change and expand the test cases in `benches/vdf/class_group.rs`. You may also need to increase pari_init size (first parameter in `pari_init`) in src/primitives/vdf.rs if testing a larger `t`. We recommend testing each case respectively (i.e., `for &i in &[1_000] {`, `for &i in &[2_000] {` ..., instead of `for &i in &[1_000, 2_000, 5_000] {`) if the memory is limited.
+
+**Usage**
+
+benchmarking class_group VDF:
+```
+cargo bench --bench bench-vdf-class  --jobs 1
+```
+
+benchmarking rsa_group VDF:
+```
+cargo bench --bench bench-vdf-rsa  --jobs 1
+```
+
 Security
 -------------------
 Security assumptions can differ between primitives and are discussed in the relevant papers. They should be understood well before using any primitive. The code is not audited and we did not attempted to make it constant time. Do not use this library in production system.

benches/vdf/class_group.rs

@@ -28,7 +28,7 @@ fn benches_class(c: &mut Criterion) {
     // change below to `for &i in &[1_000, 2_000, 5_000, 10_000, 100_000, 1_000_000] {` if needed to expand test cases,
     // may also need to increase pari_init size (first parameter in `pari_init`) in src/primitives/vdf.rs
     for &i in &[1_0] {
-        // precompute for verification
+        // precompute for benchmarking verification
         let t = BigInt::from(i);
         let vdf_out_proof = VDF::eval(&a_b_delta, &seed, &t);
         let res = vdf_out_proof.verify();

benches/vdf/rsa_group.rs

@@ -0,0 +1,134 @@
+#[macro_use]
+extern crate criterion;
+
+use criterion::Criterion;
+use rug::{integer::Order, Integer};
+use sha2::{Digest, Sha256};
+
+/// algo_2 from the paper
+fn verify(modulus: &Integer, g: &Integer, t: u64, y: &Integer, pi: &Integer) -> bool {
+    let l = &hash_to_prime(modulus, &[g, y]);
+
+    let r = &Integer::from(2).pow_mod(&Integer::from(t), l).unwrap();
+    let pi_l = pi.clone().pow_mod(l, modulus).unwrap();
+    let g_r = g.clone().pow_mod(r, modulus).unwrap();
+    let pi_l_g_r = pi_l * g_r;
+
+    pi_l_g_r.div_rem_floor(modulus.clone()).1 == *y
+}
+
+/// algo_3 from the paper
+fn eval(modulus: &Integer, g: &Integer, t: u64) -> (Integer, Integer) {
+    // y <- (g^2)^t
+    let mut y = g.clone();
+    for _ in 0..t {
+        y = y.clone() * y.clone();
+        y = y.div_rem_floor(modulus.clone()).1;
+    }
+
+    let l = hash_to_prime(modulus, &[g, &y]);
+
+    // algo_4 from the paper, long division
+    // TODO: consider algo_5 instead
+    let mut b: Integer;
+    let mut r = Integer::from(1);
+    let mut r2: Integer;
+    let two = Integer::from(2);
+    let mut pi = Integer::from(1);
+
+    for _ in 0..t {
+        r2 = r.clone() * two.clone();
+        let quo_rem = r2.clone().div_rem_floor(l.clone());
+        b = quo_rem.0;
+        r = quo_rem.1;
+        let pi_2 = pi.clone().pow_mod(&two, modulus).unwrap();
+        let g_b = g.clone().pow_mod(&b, modulus).unwrap();
+        pi = pi_2 * g_b;
+    }
+
+    (y, pi.div_rem_floor(modulus.clone()).1)
+}
+
+/// hashing an element onto the group
+/// only run once, so won't downgrade the perfomance
+fn h_g(modulus: &Integer, seed: &Integer) -> Integer {
+    const HASH_ENT: u32 = 256;
+    const GROUP_ENT: u32 = 2048;
+
+    let prefix = "residue_part_".as_bytes();
+    let seed_bytes = seed.to_digits::<u8>(Order::Lsf);
+
+    // concat 8 sha256 to a 2048-bit hash
+    let all_2048: Vec<u8> = (0..((GROUP_ENT / HASH_ENT) as u8))
+        .map(|index| {
+            let mut hasher = Sha256::new();
+            hasher.update(prefix);
+            hasher.update(vec![index]);
+            hasher.update(seed_bytes.clone());
+            hasher.finalize()
+        })
+        .flatten()
+        .collect();
+    let result = Integer::from_digits(&all_2048, Order::Lsf);
+    result.div_rem_floor(modulus.clone()).1
+}
+
+fn hash_to_prime(modulus: &Integer, inputs: &[&Integer]) -> Integer {
+    let mut hasher = Sha256::new();
+    for input in inputs {
+        hasher.update(input.to_digits::<u8>(Order::Lsf));
+        hasher.update("\n".as_bytes());
+    }
+    let hashed = Integer::from_digits(&hasher.finalize(), Order::Lsf);
+    hashed.next_prime().div_rem_floor(modulus.clone()).1
+}
+
+fn benches_rsa(c: &mut Criterion) {
+    let bench_eval = |c: &mut Criterion, difficulty: u64, modulus: &Integer, seed: &Integer| {
+        c.bench_function(&format!("eval with difficulty {}", difficulty), move |b| {
+            b.iter(|| eval(&modulus, &seed, difficulty))
+        });
+    };
+    let bench_verify = |c: &mut Criterion,
+                        difficulty: u64,
+                        modulus: &Integer,
+                        seed: &Integer,
+                        y: &Integer,
+                        pi: &Integer| {
+        c.bench_function(
+            &format!("verify with difficulty {}", difficulty),
+            move |b| b.iter(|| verify(&modulus, &seed, difficulty, &y, &pi)),
+        );
+    };
+
+    /// RSA-2048 modulus, taken from [Wikipedia](https://en.wikipedia.org/wiki/RSA_numbers#RSA-2048).
+    pub const MODULUS: &str =
+    "251959084756578934940271832400483985714292821262040320277771378360436620207075955562640185258807\
+    8440691829064124951508218929855914917618450280848912007284499268739280728777673597141834727026189\
+    6375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172\
+    6546322822168699875491824224336372590851418654620435767984233871847744479207399342365848238242811\
+    9816381501067481045166037730605620161967625613384414360383390441495263443219011465754445417842402\
+    0924616515723350778707749817125772467962926386356373289912154831438167899885040445364023527381951\
+    378636564391212010397122822120720357";
+    let modulus = Integer::from_str_radix(MODULUS, 10).unwrap();
+
+    const TEST_HASH: &str = "1eeb30c7163271850b6d018e8282093ac6755a771da6267edf6c9b4fce9242ba";
+    let seed_hash = Integer::from_str_radix(TEST_HASH, 16).unwrap();
+    let seed = seed_hash.div_rem_floor(modulus.clone()).1;
+
+    // g <- H_G(x)
+    let g = h_g(&modulus, &seed);
+
+    for &i in &[1_000, 2_000, 5_000, 10_000, 100_000, 1_000_000] {
+        // precompute for benchmarking verification
+        let (y, pi) = eval(&modulus, &g, i);
+        let result = verify(&modulus, &g, i, &y, &pi);
+        assert!(result);
+
+        bench_eval(c, i, &modulus, &seed);
+        bench_verify(c, i, &modulus, &seed, &y, &pi)
+    }
+}
+
+criterion_group!(benches, benches_rsa);
+criterion_main!(benches);