monero_generators/
hash_to_point.rs

1use subtle::ConditionallySelectable;
2
3use curve25519_dalek::edwards::EdwardsPoint;
4
5use group::ff::{Field, PrimeField};
6use dalek_ff_group::FieldElement;
7
8use monero_io::decompress_point;
9
10use crate::keccak256;
11
12/// Monero's `hash_to_ec` function.
13pub fn hash_to_point(bytes: [u8; 32]) -> EdwardsPoint {
14  #[allow(non_snake_case)]
15  let A = FieldElement::from(486662u64);
16
17  let v = FieldElement::from_square(keccak256(&bytes)).double();
18  let w = v + FieldElement::ONE;
19  let x = w.square() + (-A.square() * v);
20
21  // This isn't the complete X, yet its initial value
22  // We don't calculate the full X, and instead solely calculate Y, letting dalek reconstruct X
23  // While inefficient, it solves API boundaries and reduces the amount of work done here
24  #[allow(non_snake_case)]
25  let X = {
26    let u = w;
27    let v = x;
28    let v3 = v * v * v;
29    let uv3 = u * v3;
30    let v7 = v3 * v3 * v;
31    let uv7 = u * v7;
32    uv3 *
33      uv7.pow(
34        (-FieldElement::from(5u8)) *
35          FieldElement::from(8u8).invert().expect("eight was coprime with the prime 2^{255}-19"),
36      )
37  };
38  let x = X.square() * x;
39
40  let y = w - x;
41  let non_zero_0 = !y.is_zero();
42  let y_if_non_zero_0 = w + x;
43  let sign = non_zero_0 & (!y_if_non_zero_0.is_zero());
44
45  let mut z = -A;
46  z *= FieldElement::conditional_select(&v, &FieldElement::from(1u8), sign);
47  #[allow(non_snake_case)]
48  let Z = z + w;
49  #[allow(non_snake_case)]
50  let mut Y = z - w;
51
52  /*
53    If sign, `z = -486662`, else, `z = -486662 * v`
54    `w = v + 1`
55
56    We need `z + w \ne 0`, which would require `z \cong -w \mod 2^{255}-19`. This requires:
57    - If `sign`, `v \mod 2^{255}-19 \ne 486661`.
58    - If `!sign`, `(v + 1) \mod 2^{255}-19 \ne (v * 486662) \mod 2^{255}-19` which is equivalent to
59      `(v * 486661) \mod 2^{255}-19 \ne 1`.
60
61    In summary, if `sign`, `v` must not `486661`, and if `!sign`, `v` must not be the
62    multiplicative inverse of `486661`. Since `v` is the output of a hash function, this should
63    have negligible probability. Additionally, since the definition of `sign` is dependent on `v`,
64    it may be truly impossible to reach.
65  */
66  Y *= Z.invert().expect("if sign, v was 486661. if !sign, v was 486661^{-1}");
67  let mut bytes = Y.to_repr();
68  bytes[31] |= sign.unwrap_u8() << 7;
69
70  decompress_point(bytes).expect("point from hash-to-curve wasn't on-curve").mul_by_cofactor()
71}
monero_generators/hash_to_point.rs

monero_generators/
hash_to_point.rs
