1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
use rand_core::RngCore;
use group::{
  ff::{Field, PrimeFieldBits},
  Group,
  prime::PrimeGroup,
};

use crate::prime_field::{test_prime_field, test_prime_field_bits};

/// Test equality.
pub fn test_eq<G: Group>() {
  assert_eq!(G::identity(), G::identity(), "identity != identity");
  assert_eq!(G::generator(), G::generator(), "generator != generator");
  assert!(G::identity() != G::generator(), "identity == generator");
}

/// Test identity.
pub fn test_identity<G: Group>() {
  assert!(bool::from(G::identity().is_identity()), "identity wasn't identity");
  assert!(
    bool::from((G::identity() + G::identity()).is_identity()),
    "identity + identity wasn't identity"
  );
  assert!(
    bool::from((G::generator() - G::generator()).is_identity()),
    "generator - generator wasn't identity"
  );
  assert!(!bool::from(G::generator().is_identity()), "is_identity claimed generator was identity");
}

/// Sanity check the generator.
pub fn test_generator<G: Group>() {
  assert!(G::generator() != G::identity(), "generator was identity");
  assert!(
    (G::generator() + G::generator()) != G::generator(),
    "generator added to itself was identity"
  );
}

/// Test doubling of group elements.
pub fn test_double<G: Group>() {
  assert!(bool::from(G::identity().double().is_identity()), "identity.double() wasn't identity");
  assert_eq!(
    G::generator() + G::generator(),
    G::generator().double(),
    "generator + generator != generator.double()"
  );
}

/// Test addition.
pub fn test_add<G: Group>() {
  assert_eq!(G::identity() + G::identity(), G::identity(), "identity + identity != identity");
  assert_eq!(G::identity() + G::generator(), G::generator(), "identity + generator != generator");
  assert_eq!(G::generator() + G::identity(), G::generator(), "generator + identity != generator");

  let two = G::generator().double();
  assert_eq!(G::generator() + G::generator(), two, "generator + generator != two");
  let four = two.double();
  assert_eq!(
    G::generator() + G::generator() + G::generator() + G::generator(),
    four,
    "generator + generator + generator + generator != four"
  );
}

/// Test summation.
pub fn test_sum<G: Group>() {
  assert_eq!(
    [G::generator(), G::generator()].iter().sum::<G>(),
    G::generator().double(),
    "[generator, generator].sum() != two"
  );
  assert_eq!(
    [G::generator().double(), G::generator()].iter().sum::<G>(),
    G::generator().double() + G::generator(),
    "[generator.double(), generator].sum() != three"
  );
}

/// Test negation.
pub fn test_neg<G: Group>() {
  assert_eq!(G::identity(), G::identity().neg(), "identity != -identity");
  assert_eq!(
    G::generator() + G::generator().neg(),
    G::identity(),
    "generator + -generator != identity"
  );
}

/// Test subtraction.
pub fn test_sub<G: Group>() {
  assert_eq!(G::generator() - G::generator(), G::identity(), "generator - generator != identity");
  let two = G::generator() + G::generator();
  assert_eq!(two - G::generator(), G::generator(), "two - one != one");
}

/// Test scalar multiplication
pub fn test_mul<G: Group>() {
  assert_eq!(G::generator() * G::Scalar::from(0), G::identity(), "generator * 0 != identity");
  assert_eq!(G::generator() * G::Scalar::from(1), G::generator(), "generator * 1 != generator");
  assert_eq!(
    G::generator() * G::Scalar::from(2),
    G::generator() + G::generator(),
    "generator * 2 != generator + generator"
  );
  assert_eq!(G::identity() * G::Scalar::from(2), G::identity(), "identity * 2 != identity");
}

/// Test `((order - 1) * G) + G == identity`.
pub fn test_order<G: Group>() {
  let minus_one = G::generator() * (G::Scalar::ZERO - G::Scalar::ONE);
  assert!(minus_one != G::identity(), "(modulus - 1) * G was identity");
  assert_eq!(minus_one + G::generator(), G::identity(), "((modulus - 1) * G) + G wasn't identity");
}

/// Test random.
pub fn test_random<R: RngCore, G: Group>(rng: &mut R) {
  let a = G::random(&mut *rng);
  assert!(!bool::from(a.is_identity()), "random returned identity");

  // Run up to 128 times so small groups, which may occasionally return the same element twice,
  // are statistically unlikely to fail
  // Groups of order <= 2 will always fail this test due to lack of distinct elements to sample
  // from
  let mut pass = false;
  for _ in 0 .. 128 {
    let b = G::random(&mut *rng);
    assert!(!bool::from(b.is_identity()), "random returned identity");

    // This test passes if a distinct element is returned at least once
    if b != a {
      pass = true;
    }
  }
  assert!(pass, "random always returned the same value");
}

/// Run all tests on groups implementing Group.
pub fn test_group<R: RngCore, G: Group>(rng: &mut R) {
  test_prime_field::<R, G::Scalar>(rng);

  test_eq::<G>();
  test_identity::<G>();
  test_generator::<G>();
  test_double::<G>();
  test_add::<G>();
  test_sum::<G>();
  test_neg::<G>();
  test_sub::<G>();
  test_mul::<G>();
  test_order::<G>();
  test_random::<R, G>(rng);
}

/// Test encoding and decoding of group elements.
pub fn test_encoding<G: PrimeGroup>() {
  let test = |point: G, msg| {
    let bytes = point.to_bytes();
    let mut repr = G::Repr::default();
    repr.as_mut().copy_from_slice(bytes.as_ref());
    assert_eq!(point, G::from_bytes(&repr).unwrap(), "{msg} couldn't be encoded and decoded");
    assert_eq!(
      point,
      G::from_bytes_unchecked(&repr).unwrap(),
      "{msg} couldn't be encoded and decoded",
    );
  };
  test(G::identity(), "identity");
  test(G::generator(), "generator");
  test(G::generator() + G::generator(), "(generator * 2)");
}

/// Run all tests on groups implementing PrimeGroup (Group + GroupEncoding).
pub fn test_prime_group<R: RngCore, G: PrimeGroup>(rng: &mut R) {
  test_group::<R, G>(rng);

  test_encoding::<G>();
}

/// Run all tests offered by this crate on the group.
pub fn test_prime_group_bits<R: RngCore, G: PrimeGroup<Scalar: PrimeFieldBits>>(rng: &mut R) {
  test_prime_field_bits::<R, G::Scalar>(rng);
  test_prime_group::<R, G>(rng);
}

// Run these tests against k256/p256
// This ensures that these tests are well formed and won't error for valid implementations,
// assuming the validity of k256/p256
// While k256 and p256 may be malformed in a way which coincides with a faulty test, this is
// considered unlikely
// The other option, not running against any libraries, would leave faulty tests completely
// undetected

#[test]
fn test_k256() {
  test_prime_group_bits::<_, k256::ProjectivePoint>(&mut rand_core::OsRng);
}

#[test]
fn test_p256() {
  test_prime_group_bits::<_, p256::ProjectivePoint>(&mut rand_core::OsRng);
}

#[test]
fn test_bls12_381() {
  test_prime_group_bits::<_, bls12_381::G1Projective>(&mut rand_core::OsRng);
  test_prime_group_bits::<_, bls12_381::G2Projective>(&mut rand_core::OsRng);
}

#[test]
fn test_pallas_vesta() {
  test_prime_group_bits::<_, pasta_curves::pallas::Point>(&mut rand_core::OsRng);
  test_prime_group_bits::<_, pasta_curves::vesta::Point>(&mut rand_core::OsRng);
}